Green’s Dictionary of Slang

(US black) to move, to go, to travel.

1928		C. McKay Home to Harlem 71: Got to final on home to her.
1944		Cab Calloway New Hepsters Dict. in Calloway (1976) 255: final (v.): to leave, to go home. Ex., ‘I finaled to my pad’ (went to bed); ‘We copped a final’ (went home).
1946		Mezzrow & Wolfe Really the Blues 218: Come on Jack, let’s final to my main stash.