Recoup

You can cast a spell using flashback even if it was somehow put into your graveyard without having been cast.

"Flashback [cost]" means "You may cast this card from your graveyard by paying [cost] rather than paying its mana cost" and "If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack."

A spell cast using flashback will always be exiled afterward, whether it resolves, is countered, or leaves the stack in some other way.