From past job experience inflatable pfds arnt seen as a DG banned from flying with. probably don't wear it while boarding though. pilot might think your having a dig at him about your confidence in his ability to keep it in the air

brother used to be issued one mandatory to wear in the chopper when flying to the offshore rigs.. ( said the thought "why we need these" tightened the cheeks every time)
I'd check with the airline still as it's been awhile since I used to load planes as a teenager