Flying US Commercial airlines with guns and ammunition is not really a big deal, as long as you know and follow the procedures. I have to fly with guns several times each year and I never have problems. Our good friend and colleague Karim Mannassa recently wrote an excellent piece on a trip he undertook with multiple handguns and ammunition. This is full of solid advice.
https://909cdb8a-ae70-4094-9bf8-6213...7e5b4949e3.pdf