First, TN is a pretty gun friendly state. Spend some time reading HERE: http://crime.about.com/od/gunlawsbystate/a/gunlaws_tn.htm
As far as flying, read HERE:http://www.tsa.gov/travelers/airtravel/assistant/editorial_1666.shtm
Also, go to your airline's website.
When you arrive at airport- gun should be unloaded. No loaded mags. Any ammo in original boxes, in gun case. Allow a few minutes extra time. Go to check in counter. When it is your turn, smile, say (write this down) "Good morning! I would like to declare an unloaded firearm in my checked baggage." DO NOT say "I have a gun."
Airline staff will probably take you to one side, have you open the case, show gun is unloaded, have you complete declaration of unloaded firearm card, which goes in case with gun, relock it, hand case to TSA person for screening. and pay airline for the checked bag.
On arrival, your case MAY be on carousel, may be held at baggage office. You can open to do a brief check (yep, my gun is in there, alright) then close and relock case, leave airport.