Not really. Claude M. Simpson, The British Broadside Ballad and Its Music, 1966, p.97:

"[Chevy Chase], of which there are many seventeenth-century editions, is to the tune of Flying Fame, and there are at least two other ballads reprinted in Pills [to Purge Melancholy] whose broadside editions name Flying Fame. The question then is whether the music preserved as Chevy Chase was originally known as Flying Fame or whether there were two independent tunes. The ballad from which Flying Fame or When flying fame takes its name is lost; moreover, no music with those titles has survived. We can be sure, however, that Flying Fame was known as a tune when the broadside texts of Chevy Chase began to be issued. And whereas Chevy Chase continued to be named as a tune for new ballads throughout the eighteenth century, Flying Fame is found only on reissues of old ballads. We may conclude that the older tune virtually died with the seventeenth century or that the great popularity of the Chevy Chase ballad produced a new name for the tune which gradually displaced the old name. The latter hypothesis seems the more probable, but it must be kept in mind that we do not have the evidence for a positive conclusion."

He adds a footnote:

"The phrase "flying fame" occurs in two poems in A Gorgeous Gallery of Gallant Inventions, 1578, ed. Rollins, p. 61: "If that the flying fame thereof, to others eares attayne," and p. 120: "That dare I not? for feare of flying fame." The currency of the phrase tells us nothing specific about the lost ballad, but from other evidence we can be reasonably sure that it was a product of the Elizabethan muse."