In 1831 Thackeray lamented, "I was in love with two young ladies - but the day dream hath passed away, & I am left without a flame." In fact, Elvis's "(Marie's the Name of) His Latest Flame" goes back to the 14th century when flame meant passion itself before - with Cowley - becoming the object of passion. The OED's last citation is a later, 1840 one by Thackeray, and calls our use of it jocular - but Otto Harbach's lyric for "Smoke Gets in Your Eyes" is far from it.
D. J. TAYLOR'S new life of Thackeray does not mention Elvis Presley, but could reasonably do so. This is neither to reveal that the King had a passion for Vanity Fair nor to urge a biographical method akin to the wilder shores of Peter Ackroyd or of Edmund Morris's Ronald Reagan.