Perhaps the biggest advantage of integrating Kotlin using a test-first approach is that it's safe. You're not slowing down feature development through migration or refactoring and you're not shipping a new language to production users; it frees your team so that they're able to try the language without much impact on what is actually shipped.
One benefit of writing tests with Kotlin is that it can help expose stability and interop issues in your Java and Kotlin code. By exercising your code through tests, you can ensure you're using language features correctly and examine how they work from both Java and Kotlin. This can illuminate where you want to modify and how you write your code based on whichever level of interop support you need.
Kotlin can be largely beneficial for testing, irrespective of whether it's your first choice. The ability to write DSLs in Kotlin means we can write test code that is very fluent and expressive, making it easier to write, read, and validate. By reducing boilerplate and increasing readability, we can encourage developers to write tests with a lower barrier to entry.