check out the tsa site for info on taking a firearm on a plane.
http://www.tsa.gov/travelers/airtravel/assistant/editorial_1188.shtm
when you check it they are going to have you open the case, show its broken down and not loaded.
place an orange card signed by who witnessed it in the case, and have it locked.
( not depending on the airport ) someone from delta will take the gun case ( and you ) to TSA and they will x ray it and inspect it again. lock it and in some cases it goes to baggage from there, in other cases it goes back to the ticket counter ( all in the care of a airline employee and you in tow)
and gets checked with your other bags.
I dont recall what the regs were on muzzle loader as far as precussion caps, and powder, you may end up buying that at your location ( actually would suggest that )
also there is tsa approved locks. you keep the key, but the inspectors have a master that will open the locks and not destroy them. put those on your gun case. we got home from canada and when we opened up our bow and rifle cases, there was cards inside stating we had been spot inspected by TSA. they used their master keys to access our gear. ( in part because it was international ) but they do spot checks. if you lock it with a diffrent lock / they can and will cut them off to check your bags.
good luck on your hunt.