If your camping adventure begins with a flight, follow the Transportation Security Administration's rules or risk having to leave your gear at the airport. You're allowed to check your camp stove or bring it on board.
Before you leave for the airport, thoroughly clean your camp stove. The TSA doesn't allow any fuel or even fumes to get through the security line. Only empty fuel or propane tanks are allowed.
Your emptied, cleaned camp stove can go in your checked luggage. Empty propane tanks are allowed but not tanks with any fuel in them. You have to ship tanks beforehand or buy new ones at your destination.