"Do not quench the Spirit. Do not despise prophetic utterances. Test everything; retain what is good" (1 Thess. 5:19–21). I don't see anything in Scripture which says prophecy ends with the death of the last apostle, though it is true that these prophecies add nothing to the Word, but only help to clarify it, sort of like how God uses everyday life to bring us to Christ. Cf. Jude 3. (Neither do I see Sola Scriptura in Scripture. Cf. 2 Thes 2:15.) Historically, the Church's tradition is to test prophecies (private revelations) against the Word of God. Here is a sampling of the respectable fathers on private revelations or prophecies:

Hermas

"The vision which I saw, my brethren, was of the following nature . . . [An] old woman approached, accompanied by six young men . . . [And] she said to me . . . ‘Lo! do you not see opposite to you a great tower, built upon the waters, of splendid square stones?’ For the tower was built square by the six young men who had come with her. But myriads of men were carrying stones to it, some dragging them from the depths, others removing them from the land, and they handed them to these six young men. . . . [And the woman said:] ‘The tower which you see building is myself, the Church . . . the tower is built upon the waters . . . because your life has been and will be "saved through water" [1 Pet. 3:20–21] . . . the six young men . . . are the holy angels of God . . . the other persons who are engaged in carrying the stones . . . also are holy angels of the Lord . . . [And] when the tower is finished and built, then comes the end’" (The Shepherd 1:3:1–8 [A.D. 80]).


The Martyrdom of Polycarp

"While he [Polycarp] was thus at his prayers, three days before his arrest, he had a vision in which he saw flames reducing his pillow to ashes; whereupon he turned to his companions and said, ‘I must be going to be burnt alive.’ . . . [After his arrest, the crowd called] loud demands for the Asiarch Philip to let loose a lion at Polycarp. However, he told them that the rules would not allow him to do so, since he had already declared the beast-fighting closed; whereupon they decided to set up a unanimous outcry that he should have Polycarp burnt alive" (Martyrdom of Polycarp 5, 12 [A.D. 155]).

"Polycarp was . . . bishop of the Catholic Church at Smyrna, and a teacher in our own day who combined both apostle and prophet in his own person. For indeed, every word that ever fell from his lips either has had or will have its fulfillment" (ibid., 16).


Justin Martyr

"For the prophetical gifts remain with us [Christians], even to the present time. And hence you [Jews] ought to understand that [the gifts] formerly among your nation have been transferred to us" (Dialogue with Trypho the Jew 82 [A.D. 155]).


Irenaeus

"In like manner we do also hear many brethren in the Church who possess prophetic gifts and who through the Spirit speak all kinds of languages and who bring to light for the general benefit the hidden things of men, and declare the mysteries of God" (Against Heresies 5:6:1 [A.D. 189]).


Pionius

"I, Pionius, have made a fresh transcript of [The Martyrdom of Polycarp]. I found them after Polycarp the Blessed had revealed their whereabouts in a vision, as I will explain hereafter. Time had reduced them almost to tatters, but I gathered them carefully together in the hope that the Lord Jesus may likewise gather myself amongst his elect into his heavenly kingdom. To him, with the Father and the Holy Spirit, be glory forever and ever. Amen" (Martyrdom of Polycarp, copyist note 2 [A.D. 250]).

Anthony of Egypt

"[Anthony told his monks:] When, therefore, they [demons] come by night to you and wish to tell the future, or say ‘We are the angels,’ give no heed, for they lie. . . . But if they shamelessly stand their ground, capering, and change their forms of appearance, fear them not, nor shrink, nor heed them as though they were good spirits. For the presence either of the good or evil by the help of God can easily be distinguished. The vision of the holy ones is not fraught with distraction: ‘For they will not strive, nor cry, nor shall anyone hear their voice’ [Matt 12:19; cf. Is. 42:2]. But it comes quietly and gently that an immediate joy, gladness, and courage arise in the soul. For the Lord who is our joy is with them, and the power of God the Father" (Ambrose, Life of St. Anthony 35 [A.D. 359]).