I really don't see what John Travolta has to do with this topic, but....
From the FAA Database he has....
Private Pilot certificate for
single and multi engine land aircraft
with instrument rating.
He has type ratings in
B707, B720, CE-500, G1159, HS-125 and LR-JET
Limitations on his certificate are
CE-500 VFR Only
B707 SIC priveleges only
That is from the FAA on their own website.
He also employs a professional crew to fly the aircraft when needed or when he prefers to be with his guests in the back.