There definitely is a problem, as can be seen e.g. here: https://discuss.kotlinlang.org/t/jdk-8-compatibility-of-kotl...
Quoting: "Sometime ago we introduced kotlin.Stream<T> type, with the simples possible interface – iterator() function – with the idea that we can make it compatible with Java8 Stream<T> type. Currently we seem to come to a conclusion it was a mistake as we cannot fine a way to represent Stream<T> as kotlin type in Java 6 & 7, and then use to Java8's Stream<T> when targeting JDK8. If you have any idea about how to make it work – please share!"
Basically, while Kotlin is more or less a straightforward extension of the Java 6'th Collections APIs, by Java 8's release the two have diverged. When programming in Kotlin, you would normally use its own functional APIs, not Java Streams API. While technically nothing prevents you from using Streams, they don't fully integrate with Kotlin's native Collections, so you're forced to choose one or another.