A GA CCL/GAFL is recognized by like 15 or so other states. REGS State you can carry ammo in the same locked case as a firearm; however, everytime I have flown I always seperate the two. You can ship ammo in an unlocked luggage bag.

http://www.ok.gov/cleet/documents/airplane%20faq.pdf

Here is a good document to look over to get an idea of the law. Make sure that the lock and case is a good one. Alot of people will but those cheap aluminum cases from bass pro and you can drop most of them from about 15' and they will break at the hinges. Make sure that you have travel insurance or can pay to insure your bags from the airline. They will pay for lost luggage but not usually lost firearms.

When I go hunting out west I have never had a problem in the 5-6 trips I have made. Most of the time when you check your firearm they will have an air marshall or a certified "inspector" check to verify that the weapon is unloaded and they will put an inspection ziptie (thats what it looks like) to show that it wasnt tampered with at any time. Anywho.. Best of luck