From Father to Son

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

You must still follow any timing restrictions and permissions, including those based on the card's type. For instance, you can cast a sorcery using flashback only when you could normally cast a sorcery.

"Flashback [cost]" means "You may cast this card from your graveyard if the resulting spell is an instant or sorcery spell 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."