When you play a spell from trash with Kai'sa Evolutionary, can you banish it with Jhun's legend ability?

No, you cannot banish the spell with Virtuoso (Jhin's legend ability) in this scenario.

According to RiftJudge FAQ #9409, the interaction between Kai'Sa, Evolutionary and Virtuoso functions as follows:

The Sequence of Events

1. Conquer Trigger: Kai'Sa's "When I conquer" ability is placed on the chain.
2. Resolution of Kai'Sa: As her ability resolves, you play the spell from your trash. The spell is placed on the chain.
3. Spell Resolution: The spell resolves normally and moves to the trash.
4. Kai'Sa's "Then" Instruction: Kai'Sa's ability includes the mandatory instruction "Then recycle it." This moves the spell from the trash to the bottom of your deck.
5. Virtuoso's Trigger: Only after the spell has finished resolving does Virtuoso's "When you play a spell" ability trigger.

Why you cannot banish it:

By the time Virtuoso's ability triggers and is placed on the chain, Kai'Sa's ability has already finished resolving, which includes the mandatory instruction to recycle the spell. Because the spell has already been moved to the bottom of your deck, it is no longer in the trash and is no longer a legal target for Virtuoso’s banish effect.