Oh boy, oh boy! This is a topic I'm particularly interested in (as with all Kennedy topics). Obviously the OP's map is way off, but no harm done. The first thing to do when looking at a possibly JFK Jr. White House run is establish his entrance into politics. The POD would be the fateful flight to Martha's Vineyard. If Kennedy lands safely, than he goes on to the wedding and possibly bigger, better, things. His first incursion into popular politics would likely be a run for the Senate in 2000 for the retiring Daniel Patrick Moynihan's seat. Kennedy's immense personal popularity and likability means that Hillary Clinton might forego a run in favor of pursuing a more winneable race (such as the 2002 Illinois Gubernatorial Election). If that's the case, than Congresswoman Nita Lowey (a potential candidate in OTL) runs. Kennedy beats her, and then faces off against either Giuliani or Lazio in the general election. Either way he wins, but if it's Giuliani than it's a somewhat closer race.
Once in the Senate, John John would attempt to straddle the benefits of being mentored by his liberal uncle with the electoral realities that a hard-left voting record is a hard sell. He votes against both Bush Tax Cuts, CAFTA, and both the gay marriage and partial-birth abortion bans. At the same time, I could imagine him going either way on the Iraq War issue, while strongly supporting the War in Afghanistan. He has a similar voting record to Clinton's IRL, but his focus is probably more devoted to foreign policy than health care. In 2004, he is on John Kerry's VEEP shortlist, but is passed over in favor of John Edwards in an attempt at regional balance. JFK is reelected by a wide margin in 2006.
As far as 2008 goes, I would imagine Kennedy runs for the Democratic Nomination. It's quite possible that Obama foregoes the race due to a couple of reasons: 1) both Obama and John John are charismatic young Senators, 2) the two may have become good friends while in the Senate and would avoid a confrontation, or 3) Clinton ran for the Illinois Senate Seat in 2004 and won. Therefore Kennedy faces off against Clinton (either in the capacity of Governor of Illinois or Senator), Edwards (if he is still Kerry's running-mate), and several other candidates (it's possible that Feingold, Kerry, Bayh, or Warner run if neither Kennedy nor Clinton are viewed as insurmountable frontrunners). There's no guarantee that Kennedy wins the nomination, but if he does it's likely he chooses a moderate governor like Brian Schweitzer or Ted Strickland to balance the ticket. In the November elections, he defeats any GOP nominee due to Kennedy's charisma and the economic collapse. Here is a potential map:
Once President, Kennedy appoints a cabinet of Washington insiders and Kennedy allies. He follows a similar course on most issues as Obama has, but maybe not as vigorously on health care reform (than again, maybe more so because of his uncle's focus on that issue). There is less dissapointment aimed at Kennedy, due to the fact that he didn't have the same aura of Change that Obama did. Either way, his approval ratings aren't great, 2010 is a rough mid-term cycle, and 2012 will be a tough battle.
