Green’s Dictionary of Slang

the potential victim of a confidence trickster.

1812		Vaux Vocab. of the Flash Lang. in McLachlan (1964) 241: flat: In a general sense, any honest man, or square cove, in opposition to a sharp or cross-cove; when used particularly, it means the person whom you have a design to rob or defraud, who is termed the flat, or the flatty-gory.
1835		Metropolitan Mag. XIV Sept. 333: Our suit [...] got on pretty well — we served it out to three flatty-gories in the first week, clying upwards of a hundred couple of quid.