Green’s Dictionary of Slang

(US black) a sharply pleated zoot suit n.

1942		Z.N. Hurston ‘Story in Harlem Sl.’ in Novels and Stories (1995) 1002: So Jelly got into his zoot suit with the reet pleats and got out to skiwer around and do himself some good.
1970		(con. 1940s) E. Thompson Garden of Sand (1981) 428: Men in two-tone, dagger-toed shoes and drape trousers with a reet-pleat twirled four-foot watch chains, jiving the chicks.
1987		(con. 1940s) Ellroy Black Dahlia Prologue (1988) 11: Hundreds of in-uniform soldiers, sailors and marines descended on downtown LA, armed with two-by-fours and baseball bats. [...] Our service revolvers had been taken from us at the station; the brass did not want .38’s falling into the hands of reet pleat, stuff cuff, drape shape, Argentine ducktail Mexican gangsters.
2006		F.X. Toole Pound for Pound 72: Slick-dick dudes who wore zoot suits with reet pleats and drape shapes.