Is it in the hand that gets traded?

Since the card doesn't state otherwise, then yes, Trader has to trade away his Super Flare to use it. Bummer.

I don't think so. The card is in play at that point. You play the Flare, trade hands, then pick up the Flare again.

Page 13 says "Flare cards are returned to the player's hand after being played instead of being discarded."

"Returned" is the key word, meaning it is played to the table, out of hand. Since you play it to trade hands, I'd agree with Wraith that it is not in the hand that's traded for that reason and because it seems illogical when so few flares have to be discarded or given away, only the most poweful ones, and this is a pretty standard super flare (not that it's by any means weak).