Green’s Dictionary of Slang

(US Und.) a side pocket.

1914		Wash. Post 11 Nov. Miscellany 3/4: Pockets range from ‘side kicks’ to ‘double insiders,’ which are the inner vest pockets.
1935		(ref. to 1910) D. Maurer ‘Lingo of the Good People’ AS X:1 20/2: Side-kick [formerly] one’s pal. In modern argot a side pocket in the coat; it is doubtful if there is any connection.
1950		Goldin et al. DAUL 194/1: Sidekick. 1. (Among pickpockets) Outside coat pocket; vest pocket.
1955		D. Maurer in PADS XXIV. 125: The outside pockets in an overcoat are called side kicks (from which we get a venerable American idiom).