A client recently asked me whether he could carry a firearm on an aircraft. As usual, my lawyerly answer was "it depends". What does it depend upon? Well, for starters, what type of firearm? Will it be carried concealed or on the person (e.g. using a concealed carry weapon "CCW" permit), or will it be in checked luggage? What type of aircraft? Is it a commercial flight or a private flight? Is the flight interstate or intrastate? The answers to these questions dictate whether or how you can transport a firearm on an aircraft.
Probably the best way to look at the issue is to determine where you will be with the firearm when you board the aircraft: Within a sterile area of an airport or within a non-sterile area of an airport. Several different statutes apply to transportation of firearms on aircraft, depending upon the type of aircraft and aircraft operation and where you board the aircraft.
Another regulation that affects your ability to carry a firearm on a flight operated by a charter operator is 14 CFR §135.119. Under this regulation "no person may, while on board an aircraft being operated by a certificate holder, carry on or about that person a deadly or dangerous weapon, either concealed or unconcealed. Section 135.119 does not apply to LEO's or to "Crewmembers and other persons authorized by the certificate holder to carry arms". Thus, although this regulation appears to limit the possession of firearms, if the charter operator grants you permission, either directly or within its operations specifications, you would be exempt from this regulation and able to carry firearms subject to any other applicable statutes or regulations.