Green’s Dictionary of Slang

kick v.5

(US black) to empty, to finish, e.g. a bottle of beer.

[UK]J. Mowry Six Out Seven (1994) 150: Hobbes’s laugh came from beside him. ‘That the way to slam a forty, man. Twenty say y’all can’t kick it.’ Lactmeon’s lips twisted in a smile around the bottle, and he finished the whole thing.