Green’s Dictionary of Slang

(orig. US black) boastful, noisy, verbose.

1960		C. Cooper Jr Scene (1996) 203: Why, you fat-mouthed preacher!
1974		G.V. Higgins Cogan’s Trade (1975) 110: He doesn’t get some fatmouth bastard in there, fuck things up.
1977		A. Brooke Last Toke 93: That jive, triflin’, no-account, fat-mouth bitch!
1986		J. Ellroy Suicide Hill 227: ‘[H]e’s [a] fat-mouth motherfucker, which ain’t as bad as bein’ a snitch, but still ain’t good’.