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Took American Airlines from DFW Airport to Florida and back. American Airlines does NOT require ammo in a separate case. But, ammo can't be loaded into mags and the ammo should be stored in the original box or in a box that doesn't allow the ammo to move around loosely. I had one hard Pelican case (with non-TSA keyed locks) inside one suitcase (that had TSA locks). The Pelican case was secured to the suitcase frame with a bicycle security cable. At DFW Airport, the AA rep just asked me to open suitcase and Pelican case so that they can just look at it. That was it, no other person, including a TSA rep, looked at it. You then sign a voucher that states the gun is unloaded and the voucher is taped onto the Pelican case. The entire process took maybe two minutes.

At the airport in Florida, the AA person didn't even inspect anything. They just asked me if the gun was unloaded and then handed me the voucher. Total time was one minute.

Tip: Let them know that you know what you're doing by doing this: Walk up to the counter and say, "I would like to declare a firearm. It's unloaded, packed in a hard case, and is ready for inspection."

From American Airline's website:
Within the U.S., you can only travel with firearms and ammunition, including pellet and BB guns, in your checked bags if you’re over 18 years old. You must check them with an agent at check-in and declare that you’re traveling with firearms and ammunition.

Firearms must be:
Unloaded
In a locked hard-sided container where the firearm is totally inaccessible
Rifle cases require locks on each end

Ammunition must be:
In the original packaging from the manufacturer or in packaging specifically designed to carry small amounts of ammunition (made of fiber, wood or metal), with a maximum of 11 pounds (5 kgs) per container or customer. Ammunition is not accepted loose or in magazines or clips.