If you set up a Medical ID, then thy can access it by going to the Password Screen -> Emergency -> Medical ID
They can then compare your name and other details like Date Of Birth, if you set it up and provided them when booking the flight.
Another way to prove it is if you set up Apple Pay.
If you are on iOS 12, and enabled the wallet icon on the control centre they can tap it to see what cards you have registered.
You can then tell them:
It would help a lot if the card you paid for the flight with was there as well.
If you don’t have the icon enabled, you might have the settings enabled that they can double-click on the lock screen and see the same information.
If it still has some battery charge, or they plug it in somewhere, near some WiFi, you could set it to lost mode and include your email/phone number etc on the screen message.
They should be able to turn Airplane mode off from the lock screen without unlocking it.
Lock Screen Photo
You can describe the lock screen photo especially if it is a custom image.
You can tell them the Serial Number which will be at the back of the device. This can be found on the Apple ID page.