TL;DR
We've released a persistence library for Kotlin, you can find it on our Github. It’s a JPA-to-Exposed SQL DSL generator.
The state of persistence in Kotlin
One of the key decisions that helped Kotlin gain massive popularity was to reuse Java ecosystem instead of inventing it’s own. This means that you can safely use Kotlin as a primary language for a project developed using any popular Java stack like Spring Boot and built with Java build tool like Maven. What this also means is that natural choice for persistence layer in Kotlin is Spring Data with JPA 3 with Hibernate as an implementation.
However, JPA, which highly relies on mutable objects and dirty checking, may not look like pure Kotlin, which tries to embrace functional programming and immutability. The official Spring JPA guide for Kotlin uses mutable classes and properties which is not really idiomatic for Kotlin where you want to use immutable data classes whenever it’s possible.