From the kind. It is a lexicalization of a voiced dental fricative having become a plosive and the plosive of the nasal + consonant termination having been dropped, both of which are common developments in many slang registers of English, such as AAVE.
da kine (not comparable)
da kine (uncountable)
- (Hawaii, slang) that; it; that thing.
- (Hawaii, slang) the kind of thing we're discussing (a shibboleth)
In HCE (Hawaiian Creole Englosh), da kine is used generally to mean almost anything, particularly when referring to a thing whose name is not known or whose name does not come immediately to mind.