I concur with Kennen Storm of Shurikens and use its triggered ability to target Star-Crossed in my trash; it resolves. Later in the turn, my enemy plays a spell that will kill Kennen. Can I react with Star-Crossed from my trash?

Yes, you can. Kennen gave Star-Crossed Flow this turn, granting permission to play it from your trash, and Star-Crossed has [Reaction], which lets you play it during a Closed State (while the opponent's spell is on the Chain).

Here's the sequence:

1. Opponent plays a spell targeting Kennen. That spell becomes a Finalized Chain Item, creating a Closed State.
2. You play Star-Crossed from your trash for its Flow cost (3E/1P) as a Reaction — it goes on top of the chain, targeting Kennen (friendly) and an enemy unit.
3. Star-Crossed resolves first (LIFO), returning Kennen to your hand. The enemy unit also returns to hand.
4. The opponent's kill spell resolves, but Kennen is no longer on the board — that instruction fails to find its target and is ignored.

The only catch: you need a second valid enemy unit on the board to target (Star-Crossed requires both a friendly and an enemy unit). As long as you have one, you can save Kennen cleanly.