No.

The page you link has the foundation’s leadership structure. He’s a cochair on the board with 8 total people. The board is a degree removed from day to day operations of the foundation. He’d have to convince the board to then convince the executives.

That transaction would then show up in their financial statements, which are audited and publicly posted on that website. Meaning using the foundation’s money for something like a private jet would become public knowledge within a couple years and would do irreparable harm to the foundation’s reputation.