Green’s Dictionary of Slang

kick, the n.

1. a dismissal, ‘the sack’ [SE kick; one is lit./fig. ‘kicked out’; var. on boot, the n.].

‘The Alphabet Poem’ (US Army poem) K is the Kick, that boots soldiers out.

2. (US Und.) a beating, during interrogation, by the police.

[US]C.G. Givens ‘Chatter of Guns’ in Sat. Eve. Post 13 Apr.; list extracted in AS VI:2 (1930) 133: Kick, the, n. Third degree.

In phrases

get the kick (v.) (also give the kick)

to be dismissed/to dismiss from a job.

Jamie Muse 100: She was soon to get the kick [EDD].
Fraser Poems 50: Should a brither be sick, They’ll no gie him the kick [EDD].