Actually, this probably has more to do with the airline policy. For CC signup bonuses, it would probably be found quickly via social security number.

Has it been awhile since you opened the FF accounts and which airline - it would probably be an airline specific thing. It might even be as simple as changing frequent flier account 1 (on address A) to address B and changing account 2 from address B to address A.

Does this airline's credit card ask you to enter the FF# in the application or do they do some "magic" and find it themselves?