However the Kennedy legend would be tarnished probably through Vietnam which he would become deeply involved in probably more enthusiastically than Johnson was and the demonstrators would be chanting "Hey hey JFK how many kids have you killed today!"
No, because Kennedy would not get involved in Vietnam. He was against it, fearing another Korea quagmire, he didn't even like the situation involving advisers getting the US in there to begin with and said that Ike had laid that problem on his lap, and wanted to revert to a policy of aid and supply with a full withdrawal by 1965 (McNamara thought this unfeasible and drew up a plan for full withdrawal by 1968). Kennedy also frequency fought off military men in his administration who called for greater involvement.
Johnson was many times more likely to get into Vietnam than Kennedy. He was less knowledgeable of the situation, had less foreign policy experience and credentials to wiggle out of it or know what not to do (JFK was a foreign policy wonk; LBJ was a domestic policy wonk), and was willing to listen to the military men and go in guns a-blazing. And even then, he could have avoided it easily.
A minority of the public paid attention to Vietnam, and a minority of that portion saw South Vietnam victory as the outcome of the conflict. Vietnam was a non issue, easily avoidable if one wanted to avoid it.
Another good question would there be an "alternate" Vietnam in another front such as Africa. If America isn't turned off of intervention against the Communists it's possible.
Few people remember, Korea had already been that kind of situation. It was a quagmire, very unpopular at home after a while, and the US barely won it. That's what made many anxious about Vietnam to begin with; it could have been another Korea, and it turned out to be even worse.
The US won't see as extreme an aversion, but it'll still have the lessons of Korea. And secondly, what motivation would they have to get involved in a conflict like that?
It's possible, I suppose, but not destined to happen. And Vietnam was a unique situation; it was lead by hardened nationalists and Communists and had a people who had the spirit to fight on and on to millions of casualties, and was in supply range of the Communist world.