I only have experience with this topic in Virginia. In our fair Commonwealth, the Virginia Code covers what is and is not permitted in Section 18.2-308. Last I checked, no federal laws apply. Open-carry while you fly? Sure. CCW permit with your firearm in your flight bag? Sure. The challenge one could possibly encounter is the policy of the flight school from which the aircraft is rented. Renters may be asked to refrain from carrying while on the premises. Flying with an instructor? Secure your weapon in your vehicle. Renting without an instructor? Secure your weapon in your vehicle, conduct your business in the flight school, then retrieve your weapon and go fly. When I was instructing we had a customer who was interested in carrying during lessons. There was no policy in place at the time, so they owner did some research and created one. Customers were welcome to carry as long as the instructor was comfortable with it. Unfortunately, employees were not permitted to carry.