Green’s Dictionary of Slang

1. to obtain a drink, esp. of a barman, e.g. fire me a rum.

1977		A. Clarke Prime Minister (1978) 30: Fire some more liquor before you go to eat.
1980		A. Clarke Growing Up Stupid Under the Union Jack 29: Man, fire one!
1999		K. Sampson Powder 13: Keva got up to fire them in.

2. to drink strong liquor; thus fire a booze/drink/few/rum/the grog, to take a drink.

1993		G. Pelecanos Nick’s Trip 8: [He] fired back the shot.
2000		G. Pelecanos Shame the Devil 274: Wilson fired down his cognac.
2006		G. Pelecanos Night Gardener 88: He fired it down and left the bar unsatisfied.
2009		T. Black Gutted 101: Mac poured the whisky, placed it down. I fired it, said, ‘Another like it’.