Should I rewrite the existing Java code in Kotlin?

If your existing codebase or application is already in Java then kindly don't rewrite the existing code in Kotlin, instead, you can start by writing tests for your existing application in Kotlin that way you get comfortable writing Kotlin and get test cases for your application (which you probably haven't written yet). 

Later you can write the new functionalities in Kotlin (thanks to the excellent inter-operability with Java).