Green’s Dictionary of Slang

kink n.1

[typically ‘kinky’ black hair]

(US) a derog. term for a black person.

implied in come the kink
[US]Mencken ‘Designations for Colored Folk’ in AS XIX:3 173: Kink shows an obvious allusion to the Negro’s hair.

In phrases

come the kink (v.)

to steal a black slave from the country, and dispose of them in town.

[US]J.H. Browne Four Years in Secessia 288: ‘Coming the kink’ was to steal a negro from the country, and dispose of him in town .