I got a question about this matter a few days ago.
It’s good to know if you have a trip and want to style your hair for your holiday destination.
According to Transportation Security Administration (TSA) hair straighteners (flat irons) that are powered by a plug are allowed in both carries on bags and checked bags.
Battery operated straighteners should be in carrying on bags, they are not allowed in checked bags.
Cordless hair straightener with a butane cartridge is only allowed in carry-on bags.
It should be stored in a case that prevents you from accidentally switching it on. And you can’t bring a spare cartridge.