Usage of Philanthropist Flare as Schizoid
I'll start by saying that there won't be an explicit answer to this question. Cosmic Encounter is about interactions, and given the number of aliens with different powers, sometimes you just have to make it up as you go and use some logic to come to the best conclusion. I think this is probably one of those situations.

My interpretation would be when you play the Philanthropist Flare as the Schizoid, the player you lend your power to can look at the win condition. The most logical reasoning for this is presented by dorakeen in a different answer: the player with the Schizoid power "is responsible to announce when any player(s) have fulfilled the winning conditions". When you use the Philanthropist Flare, you no longer have your power and as such cannot declare a win condition met. The person who is now the Schizoid, even temporarily, has that job.

Additionally, there's nothing on the Schizoid card that says you can't show the alternate win condition to other players. If something in the game would cause that card to be revealed to another player or players for some reason, nothing is there to stop that event. The lack of specification about whether other players could see that card leads me to believe that it could be shown.

Having said that, if you and your game group feel that the answer is actually no, there's nothing in the rules to contradict you. Remember the game is about interactions, so do what makes the most sense to you.