I've flown Frontier (ew), Delta and American.
All have the same policy.
Needs to be in a locked hard case. Pelican, yes. Factory or Plano? No.
A case that's hard and not flimsy, has holes for locks, and clips that clip tightly. Pelican is air tight. That's basically what they hint at all the time.
Ammo needs to be in a separate location in the checked bag and needs to be in the factory box that it either came in, any factory box in general, or those plastic boxes. No loose ammo.
Gun, unloaded in the case and ammo, in a factory-like packaging.
Locks! Non-TSA locks. I'll get to that in a minute.
You tell the desk agent that you have a firearm you need to declare. Most of the time they're calm and give you a tag to sign and date stating that it's unloaded and yours.
You'll either be walked to TSA where they're do one of two things.
One, they'll grab the bag after you tagged your firearm case yourself, and run it through the X-ray machine. Then you'll be on your way as normal.
Two, they'll open your bag while you're there and ask you to open the case IF they need you to. Usually they don't, at least not in my experience.
Federally only YOU can have access to your firearm. They know this. So they keys to that gun need to stay on you at all times. Anyways, they'll check through the bag and then clear you.
I lock that bag too. They ask you to open it. No biggie.
My gear, holsters, knives, flashlight without the batteries in it, (batteries are in my pocket), stays in the luggage as usual.
All done.