Can I play Fiery Flint and discard two cards if there are no cards left in my deck?
No, you cannot. Discarding the two cards is a cost not the effect, and you cannot play Trainer cards for no effect.
Source: TPCi Rules Team (2019-03-21)
Can I play Fiery Flint if I only have 1 card in my hand to discard?
No, you must be able to discard 2 cards in order to use Fiery Flint.
Source: TPCi Rules Team (2018-09-27)