In addition, Cosmic Zap can also be played by you on your own power. This adds a quirky but valuable strategy for some powers, especially when they have their own flare card. There's debate about what's supposed to happen with being able to use the Wild part of the flare in that case, but as far as I know you can use it if your power is Cosmic Zapped.
There's no debate about that; you can definitely use your Wild Flare if you've been Zapped.
The debate is about whether the "Give this Flare to the alien named on it" Wild Flares actually get handed to their owners if the alien in question has already been Zapped at the time. If so, then a Zapped alien with such a Flare can use their one-shot Wild... and still hold onto the Flare. If not, then Zapping such an alien creates a window in which such a Flare can be used and discarded safely instead of going into that alien's hands.