OK So let me set up the scenario. I have a 3 str Targ character out. I also have out Pentos, which says the following: "Response: Discard a Targ attachment (cannot be saved) from a character you control to save that character from being killed or discarded from play."

If they ambush in a Flame Kissed, and then try to use Forever Burning, can I then trigger the save response on Pentos to discard the Flame Kissed to thereby removing it from the terminal effect?

I vote no. Since the text is "discard an attachment to do ….", it's a cost. You can only pay costs with cards that you control, and your opponent's Flame Kissed isn't one of those cards.

Right in one. You cannot discard their Targ attachment as the cost of your save.

There's another reason, though. If you discard Flame-Kissed ti save the character, the attachment becomes moribund. So after the save, it is still right there, giving your character "-2 and kill," until the end of the action window. That means the character will not be removed from the terminal state and triggering the save in the first place is not allowed.