You are correct: the Checker Framework does not support Kotlin. It would be possible to add Kotlin support by duplicating some of the code that uses javac APIs. There is no conceptual barrier, but it would be quite a bit of engineering work. We would accept a pull request that did this.
The same reason applies to type-checking bytecode. However, I don't think this is as compelling a use case. The Checker Framework is a specify-and-verify tool: the programmer specifies the code's intended behavior, and the Checker Framework verifies the code. It isn't as convenient to specify code for which you don't have access to the source code, and lack of access to the source code also makes it difficult to fix bugs that the Checker Framework uncovers. But this is possible with the Checker Framework, using mechanisms such as annotation files (stub and ajava files).
-Mike