Oracle Text

Conflagrate deals X damage divided as you choose among any number of targets.

Flashback—RR, Discard X cards. (You may cast this card from your graveyard for its flashback cost. Then exile it.)

Card Rulings

9/25/2006 If X is greater than 0, the number of targets must be at least 1 and at most X. If X is 0, the number of targets must also be 0.
9/25/2006 While Conflagrate is on the stack, its mana cost will reflect the value chosen for X, even if it was cast with flashback and no mana was spent on X.