Green’s Dictionary of Slang

flame v.2

also flame it up
[flamer n.1 (6)]

(US gay/campus) of a man (whether actually homosexual or not), to look exaggeratedly ‘feminine’ in dress and style; thus flaming n., acting in an obviously homosexual manner.

[US]B. Rodgers Queens’ Vernacular 82: flame [it up] to overemphasize, often deliberately, all girlish traits attributed to the effeminate.
[US]P. Munro Sl. U.
[US]J. Keenan Putting on Ritz 85: I had no idea how straight he behaved in public or in his business dealings, but here in his toy room the flaming was enough to make you gaze apprehensively at the sprinkler system [Simes:DLSS].
[US]Eble Campus Sl. Apr. 4: flame – display homosexuality in a particularly flamboyant fashion.
[US]J. Ellroy Widespread Panic 14: A flit flamed by and ogled my piece.