He was a republican until Nixon didn’t call him when he was arrested in 1960 (Nixon didn’t think it was appropriate). Kennedy did call him and King put his support behind Kennedy and the democrats and blacks have supported democrats since.
That was MLK, Sr., who was a self-declared Republican prior to that point in mid-1960. We’ve never been able to ascertain which party Jr. supported prior to 1960. But clearly he never was one after 1960. He called Goldwater a tool of Southern racists, nevermind his support for Civil Rights (albeit opposed to the big gov’t aspects of the CRAs).