can i play reaction spell in between Kayle empowers

No — if the Kayle player chains multiple Empower activations, you never get a window between them.

Each Empower activation goes on the Chain as a Pending item. When the controller finalizes it, they retain priority as the controller of the next chain item (Rules 337.4, 340.4, 312.2.c), so they can immediately activate it again without passing (Rule 338.1.a.5). You only get to play Reactions once they pass — at which point you're reacting to the whole stack before it resolves (LIFO, so your reaction hits before the last Empower).

So: if Kayle's player taps out the full chain of three [3] costs before passing, you can't interrupt mid-chain. You can react to a single Empower if they pass after it — but not in between consecutive activations. (FAQ #11753 confirms repeated activations are legal.)