Just short of 20 years ago was checking my declared revolver to leave Mpls./St. Paul for Alaska. The ammunition was in the cartridge belt loops and they weren’t going to allow it because “that’s loose ammunition”. After a 45 minute conversation/argument between the guy, his supervisor and me they decided “oh, I guess it’s okay”. I had told them to point out in the rule book (which they had) anything to support their argument.
They generally make you have ammo in a factory box or plastic box, and I’ve only had trouble checking any gun once. Ammo in a checked bag is no problem. One American Airlines staff hassled me about ten years, but it’s definitely legal to check a legal gun between two legal places you need to travel between. TSA has actually been pretty good, but they been very thorough lately with removing the guns and all the foam and inspecting everything. The guy here definitely goofed up with how he handled checking this muzzleloader, but he also isn’t the next John Dillinger.