Is there a script that automatically plays Kyoko?

fish fish fish, fish.

Well, the audio only plays automatically on correct reading answers on vocab. You can set this in the app settings, so you don’t need a script for that.

There is a script that delays moving on to the next item on a wrong answer, I think: [Userscript] Wanikani Mistake Delay (new, version 2.x)

I don’t know about the website, but I know the Flaming Durtles app does it automatically.

This may be of use to you as well. I use it anyway.