Green’s Dictionary of Slang

flat-cock n.

[the anatomical difference]

a woman.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]Lex. Balatronicum.
[UK] ‘The New Patent Fucking Machine’ in Pearl 12 June 34: It [i.e. a mechanical dildo] beats the old ‘flatcocks’ a long way, you know the old game that I mean.
[UK]‘Walter’ My Secret Life (1966) I 18: I don’t recollect [...] that I attached any lewd idea to a girl’s piddling hole, or to their cocks being flat, an expression heard I think at the same period.

In phrases

play at flatcock (v.)

of two lesbians, to enjoy intercourse by rubbing one’s genital areas together.

[[UK]Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Flat cock [...] A game at Flats].
[UK] ‘New Year’s Day’ in Pearl Christmas Annual 27: You know girls play at flatcock, haven’t you boys ever done anything of the sort together?
[UK]‘Walter’ My Secret Life (1966) VIII 1682: Twice she played at flat cocks with a woman before me.