what is the best practice around using dates in Kotlin. Should we avoid using the Java Date or Calendar classes? What is the replacement for this? Are there any good blog posts around this topic?

There is no replacement

I'm using https://github.com/JakeWharton/ThreeTenABP which is java.time backport with a bunch of tweaks for Android

Use java.time if you have it, if you don’t use Date

Date and Calendar are fine if you are only dealing with fixed points in time (e.g exact date and time in exact timezone), but once you stray away from that, it becomes a pain