Green’s Dictionary of Slang

(US black) dressed in the height of urban fashion.

1934		M. Fulcher ‘Believe Me’ in Afro-American (Baltimore, MD) 18 Aug. 13/3: Believe me the yokels are draped down [...] and in New York they strut.
1942		Amer. Mercury July 94: draped down: dressed in the height of Harlem fashion.
1942		Z.N. Hurston ‘Story in Harlem Sl.’ in Novels and Stories (1995) 1008: Draped down: dressed in the height of Harlem fashion.