As others have said, the center flat tire is probably form the rear, and that's where it should stay. Under normal conditions, I would never remove a tire and switch it to the other wheel. Front and rear tires wear differently, and in a way suited for where they are. why mess with that?

The main and immediate concern should be handling. A tire with a flat section doesn't track as well as a tire with a well crowned profile, so putting the old rear up front might lessen steering response and contribute to high speed wobble.

Even though the OPs decision doesn't involve removing a working tire since they're both off already, I'm suggesting that he remount them where they were and where he would otherwise have left them.