Green’s Dictionary of Slang

1. a moment.

1859, 1860		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.
1882		Sydney Sl. Dict. (2 edn) 5: Kick - A moment.

2. (US black) generally any little thing or situation.

1956		E. Hunter Second Ending 329: A guy named Dizzy Gillespie [...] wears a little beard right here under his lip, a sort of goatee, a little triangular thing. We call it a ‘Dizzy kick’ in the trade.
1967		P. Thomas Down These Mean Streets (1970) 81: I felt that I belonged in Harlem; it was my kind of kick. [Ibid.] 95: I hadda pull outta this shit kick.