Need more details:
Length of flight?
Length of time to and from the airport?
Coming out of clean water or a pond?
It's not going to be easy - or cheap. You'll want a long narrow poly bin (coffin box style). Make it about 1/2 the animals length LONGER than the fish. I'd have it about 3 meter deep, and half full of water. You'll want a solid lid that can be screwed down. Depending on length of flight, battery powered air pumps mounted upside down to the inside of the lid. If a long trip, you'll want to uze compressor oxygen bottles.
You'll want to keep an eye on temp and pH (pH will tend to drop) during the trip.
Make sure to not feed the fish a couple days prior to the move.
I've moved big arapaima over very long distances, so feel free to ask more. I can try and dig out old pics of my transport bins if that would help you.