I cast a spell that would destroy my opponent's face down creature, and in response she flipped it to trigger its flip effect. Can she do that? I thought you could only do that as a Flip Summon during your Main Phase.
No, she cannot.
Monsters are only flipped face up under certain conditions:
- Flip summon - a flip summon during the main phase, like you describe in your question.
- Damage step - During the battle phase when a face down defense position monster is attacked.
- Resolving an effect - When an effect specifically instructs to flip a monster face up, or instructs you to change a face down monster into attack position, which requires the monster become face up.
Can she do that?
As per your description, No.
The reason is that probably the card you used to destroy that face down monster, does the destruction without flipping the monster, contrary to, say, attacking the monster (where it then would indeed flip).
Therefore, no flip effect is activated, as the card didn't actually flip.
As we can see from the Flip effect ruling, this only activates if the monster is flipped (by attack, summon or other effect):
This kind of effect activates when the Flip monster is flipped face-up (by battle, a Flip Summon, or a card effect).