I think if JFK lived passed 1963 and has managed to serve two terms in the White House then it's likely Kennedy will prove unpopular after sending troops into Vietnam while becomes a quagmire by the 1968 election and just as unpopular, he fails to pass significance civil rights legislation passed a bitter GOP majority Congress, etc. Even if there is no war and JFK pulls out the advisers from Vietnam, he still won't do much in his second term and won't likely succeed in passing much progressive reform such as civil rights and the great society. Johnson will be liked by the Southern GOP and be seen more progressive and strong-willed than Kennedy was. He should get the nomination in 1968.
Both Kennedy brothers will probably be seen as being very similar to one another and without Dallas and the death of his father Robert probably won't have White House ambitions. The Democratic nomination goes to Vice-President Johnson in 1968 who is more popular and either gets reelected in 1972 or Humphrey gets in 1972. I see maybe RFK running in 1976 and having some sort of chance to get the Democratic nomination, but he will lose out to Reagan as the Americans grow tired of that party and will not likely seek a bid at the Presidency after this time.