I also have the Pro Limit wingfoil session bag. It's probably impossible to keep a complete wingfoil setup in this bag within 'economy' weight limits (20-22Kg most airlines) so you may have to pay an overweight charge. It's been cheaper to fly business on shorter flights (like FRA- Canaries) as you get two free 32Kg bags. Nobody charges extra for a piece of "sports equipment" anymore, just weight.
Whatever type of padding you use for the foils, a very useful thing to keep it all together is a roll of thin plastic wrap (for food storage). Wrap wrap wrap around everything, it's cheap and keeps your padding in place. Pack your foils on your deck pad with your wetsuit in between. Wrap the board and everything with the stretchy plastic wrap.
It's an environmental disaster but the whole sport is. Figure the contents of that bag represents at least a barrel of oil, we won't talk about the flight