Hi Veets, I’m not sure of the failure pressure of the materials, but it would probably depend on how you design the seams and would take some experimentation to get right. They can be made rigid, but I’ve never made anything as small as 1″ thick.
Note that cargo holds on most airliners are pressurized, but some smaller regional aircraft have rear cargo holds that aren’t pressurized, so the relative air pressure between the inside of the inflatable padding and the atmosphere would change significantly at altitude (at a cruising altitude of about 20,000 feet the pressure would be twice as much as at sea level), so you’d have to take that into account if you plan to travel in smaller airplanes.