Is there any documentation about creating custom compilation target for Kotlin?

I don't think it's something that's easily done and documented at all.

What is your use case?

@gildor a user asked at conference; wanted to try implementing compilation in PHP

So transpiling to PHP No, it would be very big project to do that. It's one more backend for Kotlin. Now Kotlin team works on compiler refactoring to share more code between different backends, but I think even after this it would be very big project. And it's not clear why do you need this, you already can run Kotlin on server using JVM, JS and even native, so one more dynamic backend with transpiling that target server only looks not really interesting and valuable