Each copy you create because of storm will cause your magecraft abilities to trigger.

Each copy will resolve one at a time. As each copy resolves, if you discarded a nonland card, the reflexive triggered ability triggers and you pick a target to be dealt damage. That ability will resolve before you deal with the next copy of Fiery Encore.

If you have no cards in hand as Fiery Encore resolves, you won’t be able to discard a card, but you will draw a card. No damage will be dealt.