I put "w samolotem" but this was wrong. How would you say "I am flying an airplane?" (i.e. as pilot not passenger)
You can also say "Lecę samolotem" or "Pilotuję samolot".
Should be w samolocie, but samolotem is more common.
Unless you are in an airplane, the airplane is inside a spaceship, and it's the spaceship that's flying. Lecę statkiem kosmicznym w samolocie.
Why is this Instrumental case? Do you assume there is a 'z' there and go by that?
Because Instrumental is used to express using some instument/tool and it is used without any preposition.
I think this is equivalent to the English construction "I am flying by airplane".