Green’s Dictionary of Slang

1. to snub, to reject, to ignore.

1957

Laurents & Sondheim West Side Story I i: The Jets, by far in the majority, flick him off. He returns with other Sharks: they, too, are flicked off.

2. (N.Z. prison) to sell.

2001

D. Looser Boobslang [U. Canterbury D.Phil. thesis] 70/2: flick off v. to sell.

3. see flip a/the bird under bird n.²