Green’s Dictionary of Slang

(US gay) to fellate.

1766		in ‘Allen Edwardes’ Rape of India (1966) 296: ‘[N]one was more fluted & stript, nor frigg’d & bugger’d themselves nigh to Death when in Bengall, than were Messrs Van & Johnstone & Co’ [Simes:DLSS].
1957		J.M. Reinhardt Sex Perversions 48: flute, verb. To perform fellatio [Simes:DLSS].
1962		‘Edwardes’ & Masters Cradle of Erotica 324: In the classical Japanese Yoshiwara or Whores’ Quarter, little girls were kept for fellatio [...] They called their erotic trick ‘fluting’ or ‘playing the pipes’ [Simes:DLSS].
1972		(ref. to 1930s) B. Rodgers Queens’ Vernacular 33: to suck a penis [...] flute (’30s).