Luther interestingly claims himself as "Isaiah", a most excellent prophet:
"Daniel and Isaiah are most excellent prophets. I am Isaiah - be it spoken with humility - to the advancement of God's honor, whose work alone it is, and to spite the devil. Philip Melancthon is Jeremiah; that prophet stood always in fear; even so it is with Melancthon" (Table Talks, Of Gods word, XXIV).
The source given is "Table Talks, Of Gods word, XXIV." Despite the incorrect use of the plural, the source is indeed the Table Talk. The version being used appears to be taken from an early English edition of the Table Talk. An earlier English version includes a much broader context, while later English versions edit it down (see for instance, this Hazlitt 1848 edition).
In regard to the German, the text from the early English editions appear to be based on the older German edition of the Tischreden found in Dr. Martin Luthers' sämmtliche Werke, p. 132. The English (bottom of page 91) follows the same content (top of page 129) of the German. One thing the German brings out that the English does not is that the section was not one long Table Talk, but rather many separate statements that the English rendering put together as one context. When one reads the English in this edition, the entire section is headed, On Solomon's Proverbs, but obviously far more is discussed than Proverbs: Esther, Tobit, Judith, Maccabees, etc. The discussion does not flow naturally because it wasn't one natural discussion. These entries were probably put together because they similarly discuss Old Testament and apocryphal books. The Table Talk the quote under scrutiny comes from was recorded by Conrad Cordatus between 1532-1533. The German text indicates it was an isolated statement. WA TR 2 records the statements as 2296a and 2296b (p.410).
The broader contexts located in this English version and this truncated English version have no bearing on the quote. The isolated quote simply states,
Daniel and Isaiah are the most excellent prophets. I am Isaiah (said Luther, be it spoke with humility) to the advancement of God's honour (whose work alone it is), and to spite the devil. Philip Melancthon is Jeremiah; "that prophet stood always in fear," even so it is with Melancthon. [link]
The Table Talk is a collection of second hand comments written down by Luther's friends and students, published after his death. Since Luther didn't write the Table Talk, the statements contained therein are purported to have been made by Luther and should serve more as corroborating second-hand testimony to something Luther is certain to have written.
Yes, there were times in which Luther spoke of himself as a biblical prophet, but what was his prophecy? It was not the divine forth-telling the future as "thus saith the Lord," but rather the proclamation of the Word of God, not in the sense of new revelation, but the biblical inscripturated Word of God. Lutheran scholar Robert Kolb points out,
Luther had no illusions about being an Enoch or Elijah returned from the grave…. What counted for Luther- and what linked him in his own mind with Elijah- was the Word of God in their mouths. He was firmly convinced that his tongue and pen proclaimed the same Word of God which Elijah proclaimed. Only because of this could he place himself in the ranks of prophets and apostles. Thus, much of the medieval notion of the prophet was not of importance for Luther. He claimed to possess no special gift beyond the Word which had been present in the mouths of the biblical prophets. His estimate of himself, as constructive promoter of the gospel or as destructive critic of false teaching, was only and only connected with the Word of God” [Robert Kolb: Martin Luther as Prophet, Teacher, and Hero: Images of the Reformer 1520-1560 (Michigan: Baker Books, 1999), p.31-32].
What can we learn from this Table Talk statement? The statement appears to be a contrast between the personalities of Luther and Melanchthon. Simply do a search on Melanchthon and the word "timid." It's no wonder that one of the main English biographies of Melanchthon is entitled,Melanchthon: The Quiet Reformer. In letters to Melanchton, Luther refers to him as "too gentile" (LW 48:257] and that he did not approve of Melanchthon's timidity [LW 48:365]. Or, consider these other purported statements said to be from Luther about Melanchthon:
“Philip stabs, too, but only with pins and needles. The pricks are hard to heal and they hurt. But when I stab I do it with a heavy pike used to hunt boars.” [LW 54:50]
“In the Acts of the Apostles you have a description of us. James is our Philip, who in his modesty wanted to retain the law voluntarily [Acts 15:13–21]. Peter signifies me, who smashed it: ‘Why do you put a yoke on the neck of the disciples’ [Acts 15:10]? Philip lets himself be devoured. I devour everything and spare no one. So God accomplishes the same thing in two different persons” [LW 54:355].
The point of the Table talk appears to be nothing more than a comparison of the personalities of Luther and Melanchthon. There is no corroborating evidence that either Luther or Melanchthon considered themselves to be giving forth extra-Biblical new revelation as modern-day incarnations of Isaiah and Jeremiah.