I think he has a valid concern that it isn’t so much whether it is legal or not by the terms of the FAA while the aircraft is in the air. The question more comes into play when you are parked on the tarmac in a different state.
While I am not an attorney, and I am not giving you any legal advice, I do carry a lot of the time and have done a little research on this topic. From what I have found, here is my unprofessional opinion:
If you are flying within your home state, as long as you are allowed to carry in your state, you will have no problems. However, if you cross state lines with the firearm, the state where you land would need to have reciprocity with your home state. Both of these scenarios are assuming you are flying with the fiream loaded and within accessibility to you during operation of the aircraft. If you have the firearm (I am assuming a handgun) in your flight bag, the flight bag is within reach during aircraft operations, then you are considered to be carrying a concealed weapon. Further, if the flight bag is in the back of the aircraft, and you take the flight bag out upon landing, then again, the weapon is considered to be concealed.
If you want a concealed carry permit that is valid in multiple states, I would recommend getting one from Florida or Utah, as they both have reciprocity with many other states, and will issue to out of state residents. Contact me if you want more information on them, or just do a google search.
If you do not have a concealed carry permit, or are landing in a state which is one of the “non gun friendly” states that doesn’t recognize your permit, then you will need to put the firearm in a locked commercial grade container, with the ammunition locked in a separate container.
Also keep in mind any states you are overflying. If something goes wrong and you have to land in Mass for instance, the last thing you want to do is get out of the plane in a panic while still having your 500 S&W strapped across your chest. Let’s just say you won’t be leaving the state for 12 months. 
If you are moving the weapon in or out of the plane for hunting purposes, or just to go plinking, you will either need to have the concealed carry permit, have them unloaded and separate from the ammo, or be in one of the great states that don’t require any permits. However, even there it is always a good idea to keep your bazooka and the ammo in a separate container.
Now, for a little praciticality, this all assumes you are going to get ramp checked by an overzealous police officer. In most instances you shouldn’t have any problems if you leave the weapon in the plane and don’t go showing how easily you can see the laser site on the side of the adjacent 737.
Hope this helps a little.