Leaders of all churches in all eras exercise authority: when you join a church, you pledge to toe the line. You agree with their non-negotiables, and you agree to be bound by their particulars which are still considered negotiable. Even heretical churches do this.
The ECFs validated their authority based on lineage and faithfulness to that lineage's teaching.
Culled from: http://www.reformedapologeticsministries.com/2014/03/the-church-fathers-taught-sola-scriptura.html
Examples from that blog follow.
I. Ambrose (330-397)
A. Scripture is the foundation of church leaders and councils
"Further, that none may fall into error, let a man attend to those signs vouchsafed us by the holy Scripture, whereby we may know the Son" (Ambrose, Of the Christian Faith, Book I, Ch. 2, s16).
“For how can we adopt those things which we do not find in the holy Scriptures?” (Ambrose, On the Duties of the Clergy, Book I, Ch. 23, 102).
“So indeed, following the guidance of the Scriptures, our fathers declared, holding, moreover, that impious doctrines should be included in the record of their decrees, in order that the unbelief of Arius should discover itself, and not, as it were, mask itself with dye or face-paint” (Ambrose, On the Duties of the Clergy, Book I, Ch. 18. 119).
“I do not wish that credence be given to us; let the Scriptures be quoted” (Saint Ambrose: Theological and Dogmatic Works, The Sacraments of the Incarnation of Our Lord, Chapter 3, p. 224).
B. Scripture is clear on salvation
“Wherefore the Scripture plainly has called that life which is blessed, eternal life. It has not been left to be appraised according to man's ideas on the subject, but has been entrusted to the divine judgment” (Ambrose, On the Duties of the Clergy, Book II, Ch. 1, 3).
“…let us now note how clearly the divine Scriptures explain a thing about which we see philosophers held so many involved and perplexing ideas” (Ambrose, On the Duties of the Clergy, Book II, Ch 3, 8).
C. Scripture is Clear on the Trinity
“God, then, is One, without violation of the majesty of the eternal Trinity, as is declared in the instance set before us. And not in that place alone do we see the Trinity expressed in the Name of the Godhead; but both in many places, as we have said also above, and especially in the epistles which the Apostle wrote to the Thessalonians, he most clearly set forth the Godhead and sovereignty of the Father, the Son, and the Holy Spirit” (Ambrose, On the Holy Spirit, Book III, Ch. 14. 94).
II. Hippolytus of Rome (A.D. 170 – 235)
A. Scripture is the source of our piety
“There is, brethren, one God, the knowledge of whom we gain from the Holy Scriptures, and from no other source…all of us who practice piety will be unable to learn its practice from any other quarter than the oracles of God” (Hippolytus, Against Noetus, Ch. 9).
B. Churches have customs and practices
“Now, driven by love toward all the saints, we turn to the essence of the tradition which is proper for the churches. This is so that those who are well instructed may hold fast to the tradition that has continued until now, and fully understanding it they may stand the more firmly…” (Gregory Dix, The Treatise on the Apostolic Tradition of St. Hippolytus of Rome, Bishop and Martyr, [SPCK, 1937], p. 7).
Hippolytus then goes on as a manual for church practice. In other words, for him, the order of the worship service, ordaining clergy, catechesis, baptism, etc was what he meant by tradition.
[Although maybe he didn't write that particular treatise!]
C. Scripture is clear enough when you read it in context
“But let him quote the passage as a whole, and he will discover the reason kept in view in writing it” (Hippolytus, Against Noetus, Ch. 4).
III. Cyril of Jerusalem [A.D. 313 – 386]
A. Salvation depends on Scripture
-and-
B. Scripture is the foundation of creeds, traditions, councils, chatechism, etc
"For concerning the divine and holy mysteries of the Faith, not even a casual statement must be delivered without the Holy Scriptures; nor must we be drawn aside by mere plausibility and artifices of speech. Even to me, who tell you these things, give not absolute credence, unless thou receive the proof of the things which I announce from the Divine Scriptures. For this salvation which we believe depends not on ingenious reasoning , but on demonstration of the Holy Scriptures” (Cyril of Jerusalem, Catechetical Lectures, 4.17).
C. Our faith and teachings are founded on the Scriptures
“…the faith…has been built up strongly out of all the Scriptures” (Cyril of Jerusalem, Catechetical Lectures, 5.12).
“Now mind not my argumentations, for perhaps you may be misled but unless thou receive testimony of the Prophets on each matter, believe not what I say: unless thou learn from the Holy Scriptures…” (Cyril of Jerusalem, Catechetical Lectures, 12.5).
D. Believers interpret Scripture
“for the indwelling Spirit henceforth makes your mind a house of God. When you shall have heard what is written concerning the mysteries, then will you understand things which thou knew not” (Cyril of Jerusalem, Catechetical Lectures, Prologue, 6).
IV Irenaeus [A.D. ? – 202]
A. The plan of salvation is in the Scriptures
B. Curated by the will of God [via church leaders]
“We have learned from none others the plan of our salvation, than from those through whom the Gospel has come down to us, which they did at one time proclaim in public, and, at a later period, by the will of God, handed down to us in the Scriptures, to be the ground and pillar of our faith” (Irenaeus, Against Heresies, 3. 1. 1).
C. Content must be proven from the Scriptures
“Such, then, is their [Gnostics] system, which neither the prophets announced, nor the Lord taught, nor the apostles delivered, but of which they boast that beyond all others they have a perfect knowledge. They gather their views from other sources than the Scriptures” (Irenaeus, Against Heresies, 1. 8. 1).
D. Scripture purposefully has perfectly plain passages
E. Scripture interprets Scripture
“all Scripture, which has been given to us by God, shall be found by us perfectly consistent; and the parables shall harmonize with those passages which are perfectly plain; and those statements the meaning of which is clear, shall serve to explain the parables; and through the many diversified utterances [of Scripture] there shall be heard one harmonious melody in us, praising in hymns that God who created all things” (Irenaeus, Against Heresies, 2. 28. 3).
F. Scripture is clear
“…the entire Scriptures, the prophets, and the Gospels, can be clearly, unambiguously, and harmoniously, understood by all…” (Irenaeus, Against Heresies, 2.27.2).
G. The Reglua Fidei is a Scriptural Creed
‘But again, when we refer them to that tradition which originates from the apostles, and which is preserved by means of the successions of the presbyters in the Churches, they object to tradition, saying that they themselves are wiser not merely than the presbyters, but even the apostles, because they have discovered the unadulterated truth’ (Against Heresies Book III, Chapter 2, Article 2)
[...and Iranaeus tells us what that tradition is next...]
“…carefully preserving the ancient tradition, believing in
one God, the Creator of heaven and earth, and all things therein, by means of Christ Jesus, the Son of God; who, because of His surpassing love towards His creation, condescended to be born of the virgin, He Himself uniting man through Himself to God, and having suffered under Pontius Pilate, and rising again, and having been received up in splendor, shall come in glory, the Savior of those who are saved, and the Judge of those who are judged, and sending into eternal fire those who transform the truth, and despise His Father and His advent. Those who, in the absence of written documents, have believed this faith, are barbarians, so far as regards our language; but as regards doctrine, manner, and tenor of life, they are, because of faith, very wise indeed” (Irenaeus, Against Heresies, 3.4.2).
H. The Apostles' tradition is a creed built on Scripture
"The Church, though dispersed through our the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: [She believes]
in one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His [future] manifestation from heaven in the glory of the Father to gather all things in one, and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of the invisible Father, every knee should bow. . . . For, although the languages of the world are dissimilar, yet the import of the tradition is one and the same” (Irenaeus, Against Heresies, I. 10. 1, 2)
V. Justin Martyr: Scripture is clear enough
“Pay attention, therefore, to what I shall record out of the holy Scriptures, which do not need to be expounded, but only listened to” (Justin Marty, Dialogue of Justin, Ch. 55)
VI. John Chrysostom (A.D. 347-407): Prove it from Scripture
“I exhort and entreat you all, disregard what this man and that man thinks about these things, and inquire from the Scriptures all these things” (John Chrysostom, Homilies on Second Corinthians, Homily 13).
VII. Lactantius (A.D. 240-320): Scripture has it all
“we have divine testimony for everything” (Lactantius, The Divine Institutes, Book III, Chapter I).
VIII. Athanasius (A.D. 296-373)
A. Scripture is sufficient
“…the sacred and inspired Scriptures are sufficient to declare the truth” (Athanasius, Against the Heathen, Part 1.1)
B. Scripture has authority over councils
“Vainly then do they run about with the pretext that they have demanded Councils for the faith's sake; for divine Scripture is sufficient above all things; but if a Council be needed on the point, there are the proceedings of the Fathers, for the Nicene Bishops did not neglect this matter, but stated the doctrine so exactly, that persons reading their words honestly, cannot but be reminded by them of the religion towards Christ announced in divine Scripture” (Athanasius, Councils of Ariminum and Selucia, Part I History of the Councils, 6).
IX. Theophilus of Antioch (d. A.D. 181): Scripture is clear
“For those who desire it, can, by reading what they uttered, accurately understand the truth” (Theophilus of Antioch, Theophilus to Autolycus, Book 2, Chapter 35)
X. Hilary of Poitiers (A.D. 300-368): Scripture is clear
“My prime object is by the clear assertions of prophets and evangelists to refute the insanity and ignorance of men. . . “ (Hilary of Poitiers, On the Trinity, Book.I.17).