Green’s Dictionary of Slang

(US) to idle, to avoid responsibilities.

1966		Current Sl. I:1 2/1: Fart it off Don’t be concerned about it.
1967–8		Baker et al. CUSS 115: Fart off Waste time, not study.
1975		G. Underwood ‘Razorback Sl.’ in AS L:1/2 58: I’ve decided to fart off studying for the test.