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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 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.