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 for your holiday destination.
According to Transportation Security Administration (TSA) hair straighteners (flat irons) that are powered by a plug are allowed in both carry on bags and checked bags.
Battery operated straighteners should be in carry 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 acidentally switching it on. And you can’t bring a spare cartridge.