I support free speech and consider myself a libertarian, having much in common with the populist-libertarian-right, and the civil-liberties-left. But tracking a flight like this on a regular basis to this intrusive a level strikes me as downright creepy and personally invasive. Are you going to track the locations of his vehicles and where they park next? An alternative argument - if we're going to do it to him, mayb…
Problem here is that there are clearly free speech bounds, but Elon Musk has campaigned publically about being a "free speech absolutist" which would entail not curbing any form of speech.
You can always find compelling arguments for banning speech or forms of speech and we'll continue to draw and redraw lines as a society. But you can't go around claiming to have some absolute principle and then renege on it any time it hurts your feelings and continue to be respected. Can you think of anyone else who has their flights tracked? Are Bill Gates' flights tracked? Why do you think that is?
Also being a public figure means that you lose some amount of privacy. If he doesn't want all this drama he could just stop talking and being a highly prominent public figure. Now we're just going to get a flight tracking website instead, probably with new features.
I think there are at least two problems with your alternative argument, if not more. The first problem is Elon Musk is politically connected and operates in the public sphere as a highly political person. The second problem is that there isn't anything that prevents people from tracking other rich people like they do Elon, except that nobody cares about what they do because they don't do things like buy Twitter. If you want a change I think you have to make private flight information unavailable, but until then I don't see any real problem with it. Stop flying a private jet if you don't like people posting where you are flying to and from. There isn't anything that prevents someone from reporting everywhere I go except that nobody cares. Hell, I self-report it on Yelp.