I bought TSA combination locks at the local hardware store, $11.99, and they are good, because TSA in MPLS and Phoenix have master keys to open. They don't need you. By TSA LAW, your firearm case CANNOT HAVE A STICKER ON IT SAYING ITS A FIREARM, but bad guys obviously know what a gun case looks like, duh. Both places opened, swabbed for explosives and couldn't care less about the firearm, because before you get there you declare them (1 rifle) as unloaded.
I flew Southwest. I put the ammo in the same locked case which is fine by them as long as the ammo is in a shell box designed to hold the ammo, metal or paper. The ammo box doesn't need to be locked. I did additionally tape my shell box. What is NOT ACCEPTABLE IS LOOSE ROUNDS, OR ROUNDS IN MAGAZINES OR CLIPS! In MPLS I had clothes packed with my rifle also, and the guy never lifted the clothes off my rifle to look at it. The guy in Phoenix did, and complimented me for a not needed, but nice touch, yellow chamber flag in my gun with the bolt open.
What is going on currently is luggage being stolen right off the carousel. My advice is to be standing right at where the luggage comes out!