If you're talking about the http4k library style, then a lot of that is actually just fairly heavy use of FP-type practises (without the monadic stuff) - lots of composition of higher order functions/decoration and simple interfaces/typealiases along with a real synergy with the Kotlin language features.
If that's what you're after then I'd recommend just studying the http4k source and the main concepts in the core - the main functions of httphandler/filter, the HttpMessage types, and the lens packages.
You can see there quite a lot of the tricks we used to refine the APIs - like the hiding of concrete types behind factory functions in companion objects etc. We also have managed to get massive reuse of the main concepts throughout the various modules.
If there's anything you see that you don't understand then feel free to ask here! 🙃
unfortunately there is no real shortcut to this style other than study - the entire library is the result of a combination of experience, the inspirational libraries (UtterlyIdle, Finagle, Fintrospect) and merciless refactoring until the design was refined. 🙃