I'm going to make the assumption that money truly is no object. So I wouldn't be a lowly millionaire, or even a billionaire, that's not enough
First, I'd buy a few carriers just for fun, and so that I could ride a commercial airline whenever I wanted to when I felt like it. I wouldn't deal with the business side of things, I'd leave that to airline experts of course so no FTers would be harmed

It would just mean a seat on any plane any time.
I'd also have memberships with all the private jet clubs. I'd use these primarily so that I could have the quickest and most convenient access from all my places of residence to the various airports these programs serve. Then of course, I would have my own fleet of aircraft always ready to fly wherever I wanted. I'd also secure landing rights at every airport again because of the convenience of some of them.
Oh, and I would join the FF programs and buy top tier elite status for the times I used them.