You are aware that King is personal friends with Richard Nixon, right? As in, the same Richard Nixon who successfully busted Alger Hiss during the McCarthy hearings, right? That alone would make his being a Commie-anything, let alone a commie republican, extremely unlikely.
And besides, if he were a communist, please explain why he explicitly stated Communism and Christianity can never go together and implicitly condemned Communism in this essay here: http://teachingamericanhistory.org/library/document/can-a-christian-be-a-communist/
King didn’t support Nixon in his run for President. His father endorsed JFK.