You can wear a diaper on a plane.
Diapers can be worn on a plane whether you need to wear the diapers or even if you just want to wear the diapers on the plane for protection to make the flight more comfortable.
Many urinary and bowel incontinent adults and even teens and kids wear diapers on a plane and it's no issue.
If wearing a diaper on a plane as an adult and going through the TSA security, the TSA agents and security will be professional and even if they feel or see your diaper they will not say anything.
Even when they see the diapers in your carry on or other luggage the TSA agents and security will not say anything to you about it to embarrass you and other people won't care either.
I wear thick diapers on a plane and have been pat down many a times and my luggage has be checked with the diapers and no issues.
I've seen some older kids wearing diapers at the airport as well including an 8 year old boy who was wearing Pampers Baby Dry diapers as I could see the diaper peeking out of his pants as his shirt rode up.
The TSA patted him down and noticed the diaper but didn't say anything to him or his parents about it.
Diapers can also be worn on long road trips or bus trips or even train trips whether you're incontinent or not.