I have one X-men and one Brotherhood character in play. I flip Mutant Nation in my resource row.

Next turn, I only have the X-Man (the Brotherhood character was KOed). Can I flip a second Mutant Nation this turn? Does my one character fulfill the requirements of the Mutant Nation since a previous had already been played or do I physically need two characters on the field to be able to use Mutant Nation?

No, if there is a team up already in play, and you only have one character in play, you can play a 2nd mutant nation.