Now, this comes from the point of view that you can only be given one action per turn and KC Supes SP power states that you give someone an action token.
What if the new KC Supes hits Rookie Shazam, who has Protected, with doubles? Rookie Shazam would immediately take an action token from Supes Special Damage Power. Would this prevent him from taking another action token for the Protected, hence making him take the damage? Or would he be able to take the token and simply push?

if he doesn't already have a token, he could just push, since he didn't take an action your turn, he just received a token.