It certainly isn't Elvis... he came along rather late in the game to claim the title of king. Besides Elvis lived long enough to become a smarmy, over paid, overweight Las Vegas lounge lizard in a white jumpsuit.
Little Richard and Jerry Lee Lewis were also relative late comers... besides they played piano and the "King of Rock and Roll" has to be a guitar player. (See
Gavin B.'s Completely Arbitrary Rules of Rock & Roll: Statute 17:Section 42: Paragraph 5 for clarification of guitar rule)
The two most frequently mentioned "first rock and roll songs" are
That's Alright Mama, (1946) by Arthur "Big Boy" Crudup and
Rocket 88 (1951) - Jackie Brenston and his Delta Cats (Jackie Brenston and his Delta Cats was actually the Ike Turner Band playing under a pseudonym).
Rocket 88 is closer to a blues boogie than rock while
Rocket 88 has a full rock and roll backbeat. Neither can claim to be king for different reasons: Crudup never really had another hit record and Ike Turner met Tina and started playing R&B and soul music, leaving rock and roll behind forever.
I think it's between Bill Haley and the Comets and Chuck Berry both of whom came along early in the game and had a lot of best selling singles. Another contender would be Buddy Holly who was a late comer but he was the most talented singer, songwriter and performer of all of the first generation rock and rollers.