I've flown with guns many, many times. Have them unloaded in a locked, airline-approved case. If it is a small pistol case, have that case in the top of your actual luggage, ie. duffle bag etc.

Check your bags at the counter, and tell the nice agent that there is a firearm in the bag. They will check you on in, then send you with that one duffel and pistol case to TSA. TSA will take it, check it, and handle it from there. When TSA is done with you, go on about your business, you're done. You'll collect it in the duffel on the other end of your flight from the baggage carousel like any other bag. Easy Cheasy