Green’s Dictionary of Slang

to swindle, to defraud, to trick.

1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant.
1896		W.C. Gore Student Sl. in Cohen (1997) 5: flim [...] to cheat.
1914		Jackson & Hellyer Vocab. Criminal Sl. 34: flim [...] To swindle; to defraud. Used especially by short-change experts.
1920		Ade Hand-made Fables 181: The Loved Ones felt that they had been double-crossed and flimmed.