Folk Medicine

"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."

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

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