Duelist's Flame

If the exiled card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

You cast the exiled card while the triggered ability ability is resolving and still on the stack. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those to cast the spell.