Green’s Dictionary of Slang

(US) complaining.

1887		G. Devol Forty Years a Gambler 90: The kicking contractor went to his room, and we held the fort.
1943		M. Curtiss Letters Home (1944) 14 Mar. 232: The attabrine was bitter naturally but if it keeps away malaria, I’m not kicking.
1949		‘Hal Ellson’ Duke 41: ‘How are you doing, Duke?’ ‘Not kicking.’.