Green’s Dictionary of Slang

fainting fits n.

[rhy. sl. = tit n.2 (1)]

the female breasts.

[UK]Daily Tel. 17 Sept. n.p.: fainting fits = the bosom.
[US]Maledicta II:1+2 (Summer/Winter) 118: Elsewhere Aylwin lists a few more ‘Vulgarities’: [...] words for breasts (brace and bits, east and west, Jersey City, thousand pities, towns and cities, fainting fits).
D. Shaw ‘Dead Beard’ at www.asstr.org 🌐 I get down close to Dionne’s fainting fits and give them a captain cook: the tips are sticking out like cigar butts.