Lets imagine that for one moment that a Senator JFK Junior runs for President in 2000. Lets say Bill C was removed from office a couple of year prior. Could he win the nomination? Which kind of platform could he run on? And could he defeat Bush?
You are asking a 4 variable supposing, which nearly makes it impossible to speculate.
1. John Kennedy Jr gets elected to the Senate.
2. He runs for President in 2000
3. Clinton has been successfully impeached.
4. He wins the Democratic nomination.
To just give you sense of the problems: look seriously at #1
What state? Mass has his uncle Ted as a Senator, two Kennedy's really isn't going to happen. New York? D'Amato's seat is possible; he did barely win re-election in 1992, however, regardless of charisma and name, Kennedy at 31 was a fledgling prosecutor in Manhattan - rather unlikely he would be a candidate; and running in 1998 would almost certainly preclude a Presidential run just before the start of the 2000 election cycle.
I could go on, but I imagine others will point out the problems. But as I said to start, constructively, your scenario assumes far too many events lining up just the right way.
By the way, a candidate's platform is really immaterial, a pro forma window dressing of modern politics.
As pointed out by Vidal, New York had a very deep Democratic bench. John Kennedy Jr.'s background wouldn't be enough. Perhaps in Mass.I think 2000 is too early, but what about him entering NYC politics at a young age? How many positions are there on the NYC city 'council', and could he dabble in one of those as a young man? He might then take the next steps, perhaps NY state office then the Senate.
Theres no room for JFK Jr in NYC municipality/city? Or State?