It is almost never a good idea to close existing credit cards, as doing so brings down your total available credit and average account length, which hurt your credit score. I personally wouldn't close any card that's been open for more than a year.

If the airline/hotel program allows only one open card at a time to qualify for the bonuses, you can simply convert the existing FF card to a non-FF card offered by the same issuer (citi, Amex, etc.) If multiple cards are allowed, you don't even have to convert--just leave the card in your sock drawer and forget about it.