Whoa, now that sounds like the use case I've been looking for since I jailbroke mine.
I have calibre set up to just email books to my Kindle, but that's an extra layer of indirection that I really don't need. I'll have to check that out.
If you have calibre, just turn on the wireless connection and have your Koreader connect to it.
I too have heard about syncthing for the first time today but from a different submission[0] you might care to be aware of.
Although, I realize Android != Kindle's OS, so I'm not sure how much concern there should be.
[0]: https://news.ycombinator.com/item?id=46184730 "Syncthing-Android have had a change of owner/maintainer"