The abbreviation of Gillian, figuratively used for woman. Every jack has his gill; i.e. every jack has his gillian, or female mate.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Gilflurt * GillsNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes