1959, American English, originally teenager or beatnik slang, possibly a shortening of cuckoo.
Using the newest show-business jargon, Tammy [Grimes] admits, "I look kooky," meaning cuckoo. ["Life" magazine, Jan. 5, 1959]
Crazy; eccentric; dippy, goofy: make you seem a little kookie/ the kooky stunt so pleased him (1950s+ Teenagers)