Yes.
a successful feint causes them to be Flat-footed, so it doesn't care if they are flat-footed already or immune to flat-footed.
Feinting is a standard action. To feint, make a Bluff skill check. The DC of this check is equal to 10 + your opponent's base attack bonus + your opponent's Wisdom modifier. If your opponent is trained in Sense Motive, the DC is instead equal to 10 + your opponent's Sense Motive bonus, if higher. If successful, the next melee attack you make against the target does not allow him to use his Dexterity bonus to AC (if any). This attack must be made on or before your next turn.
When feinting against a non-humanoid you take a –4 penalty. Against a creature of animal Intelligence (1 or 2), you take a –8 penalty. Against a creature lacking an Intelligence score, it's impossible. Feinting in combat does not provoke attacks of opportunity.
Starting at 4th level, a rogue can react to danger before her senses would normally allow her to do so. She cannot be caught flat-footed, nor does she lose her Dex bonus to AC if the attacker is invisible. She still loses her Dexterity bonus to AC if immobilized. A rogue with this ability can still lose her Dexterity bonus to AC if an opponent successfully uses the feint action (see Combat) against her.
Feinting a target does not make them Flat-footed. It simply makes them lose their Dexterity bonus to AC.
But yeah, you can normally feint any target as long as they're not mindless. Regardless if they're flat-footed or have already lost their Dex to AC. (since there is no such restriction on feinting in the feint description)