I'm actually in the process of doing what you want to do. Road so far: moved team of 5 devs (including myself) to Kotlin. Initial adoption was a bit hesitant, but after a while everyone got on board.
Our team is one of half a dozen teams in the company. Currently we still maintain the rule of using Kotlin only for the code owned by our team, but other teams are interested in switching at some point too.
Most of the challenges were related to Spring, Hibernate and Jackson, almost all of them were resolved by Kotlin team and respective frameworks' libraries' teams. Currently we hardly ever encounter any Kotlin-specific problems, except when migrating to a new version (which is generally the case with any library, language or framework).