If I play Hidden Blade on an opponent's unit at a battlefield and they use flash to prevent it from dying, does the Hidden Blade count as being played for my Ravenbloom Student?

Yes, your Hidden Blade counts as being "played" for your Ravenbloom Student, even if the target becomes illegal and the spell fails to kill the unit.

According to Rule 359.3.e.10, a spell is considered "played" once it resolves, even if none of its instructions are executed due to targets becoming invalid. Because Ravenbloom Student triggers "When you play a spell," it checks for the completion of the spell's resolution.

Sequence of Events:

1. You play Hidden Blade targeting an opponent's unit at a battlefield. It enters the chain.
2. Your opponent reacts with Flash, moving their unit to their base.
3. The chain resolves (LIFO):
   • Flash resolves first: The unit is moved to the base.
   • Hidden Blade resolves second: It attempts to execute its instruction ("Kill a unit at a battlefield"). Because the target is no longer at a battlefield, the instruction is ignored (it mistargets).
4. Spell Resolution Completes: Even though the spell had no effect, it has finished resolving and is now considered "played."
5. Ravenbloom Student Triggers: Because you successfully played a spell, the "When you play a spell" ability triggers and is placed on the chain.

Summary: The key distinction is that "playing" a spell in Riftbound is defined by the spell successfully resolving (as clarified in FAQ #689 and FAQ #9548). Since Hidden Blade resolves (even if it fails to kill the unit), the condition for Ravenbloom Student is met.