Someone is attacking my battlefield and I have the legend Ahri. My Ahri legend ability gives an enemy unit -1. If my opponent uses Flash, does the -1 still apply?

Yes, the -1 might effect from your Ahri Legend will still apply to the unit, even if your opponent uses Flash.

Here is the breakdown of why this happens:

1. Triggering: Ahri's ability triggers the moment an enemy unit gains the attacker designation at a battlefield you control.
2. The Chain: Once triggered, Ahri's ability is placed on the chain.
3. Flash: If your opponent plays Flash in response to that trigger, Flash is placed on top of the chain.
4. Resolution: The chain resolves in reverse order (LIFO - Last In, First Out).
   • First, Flash resolves, and the unit is moved to the base.
   • Then, Ahri's ability resolves. Even though the unit is no longer at the battlefield, the ability has already triggered and locked onto that unit. It will successfully apply the -1 might effect to that unit for the turn.

According to Rule 359.3.f.4, information referenced by a triggered ability (like the identity of the unit that attacked) is checked when the ability triggers. Because the ability already triggered when the unit attacked, moving the unit with Flash does not prevent the ability from resolving and applying its effect.