No problems, but you need to check ahead as noted above. I've done this for years on charters and such.
US FAA permits -
One self-inflating lifejacket or safety vest fitted with no more than two nonflammable gas cartridges for inflation purposes, plus no more than two spare gas cartridges. The safety jacket/vest must be packaged to prevent accidental activation. Airline approval required. https://www.faa.gov/about/initiatives/hazmat_safety/
Each country has their own air regulations
so check with the particular countries you are going through.
As to the airlines, they post their requirements on-line, and that governs what flight-crew permits. Most US airlines permit
PFD's either on-board or checked. In the end, it's not the airport
that determines what is safe, but the combination of the regulations
and the flight-crew.
So your homework is to (1) check both national regulations and individual airlines, and (2) remove the CO2 canister from your PFD
to make sure they cannot inflate. After you get the correct page, print several copies out, and put a page in with the checked luggage on top of your PFD and carry another with you. Sometimes the local gate agent or security guy has never heard of inflating PFD's and is just erring on the side of caution. Showing them their own regulations / company guidance eases everyone's concerns. Whatever you do, do not try to use 'logic' such as "there are already hundreds of inflating PFD's on board the aircraft". This is just counterproductive. Give yourself 15 extra minutes, and ask to talk to supervisors about what is permitted.