Green’s Dictionary of Slang

1. (US) to speak up, to tell the truth.

1907		D. Runyon ‘The Defence of Strikerville’ in From First To Last (1954) 15: I failed to hear anyone kick in with their right name.
1917		Van Loan ‘The Last Chance’ in Old Man Curry 112: He didn’t kick in wit’ that alibi because he loves me any too well.
1939		Howsley Argot: Dict. of Und. Sl.

2. (US black) to express oneself.

1995

L. Stavsky et al. A2Z.