If I use Crescent Strike on a unit and my opponent flashes out, does the damage follow?

No, the damage does not "follow" the unit if it moves to a different location.

When you play Crescent Strike, you choose a battlefield and one specific enemy unit at that location as the primary target.

If your opponent reacts by playing a card like Flash to move that targeted unit to their base (or any other location) before Crescent Strike resolves:

1. Primary Target: When the spell attempts to resolve, it checks for the target at the chosen battlefield. Because the unit is no longer there, it is no longer a legal target for the 4-damage portion of the spell. No damage is dealt to that unit (per RiftJudge FAQ #1794 and #2967).
2. "Other" Units: The 1-damage effect hits "each other enemy unit" at the chosen battlefield. Since the spell resolves at the originally chosen battlefield, it will still deal 1 damage to any other enemy units that remain at that specific location. The unit that was flashed out will not be affected by this, as it is no longer present at that battlefield.

Sequence of Events:

1. Chain State: You play Crescent Strike, choosing a battlefield and an enemy unit. The spell enters the chain.
2. Response: The opponent plays Flash in reaction, moving the targeted unit from the battlefield to their base.
3. Resolution (LIFO):
   • Flash resolves first, successfully moving the unit.
   • Crescent Strike resolves. It checks for the target at the chosen battlefield. Finding no legal target, the 4-damage instruction fails (it "mistargets").
   • The spell then proceeds to its next instruction: "Deal 1 to each other enemy unit there." It deals 1 damage to any remaining enemy units at the chosen battlefield.

This interpretation is consistent with RiftJudge FAQ #1794 and #2967, which clarify that if a unit is moved out of the required zone (a battlefield) in response to a spell that targets it there, it becomes an invalid target and the damage does not resolve.