Calibre + DeDRM should be able to remove the DRM. I haven’t needed this for some time now, so I don’t know if things have changed.
The main problem is getting the book files. You cannot transfer them from Kindle (unless maybe if it’s jailbroken), Amazon removed the possibility to download them from their page, and there is no Linux version of the Kindle app. You need to use a specific old version of the Kindle app to download the books, so that it downloads files with older DRM. Also, some newer books (books released within the last year or two, or so) might have a DRM that cannot be broken.
I think the version of Kindle app you need to use is 2.4. You can download it from here (it’s a direct download link from amazonaws). It installed and launched with Wine 11, but I don’t know if it works beyond that. After installing it, make sure you go to Tools -> Options, and deselect the setting for automatic update.
If that app works, use it to download your books, locate them on disk and then drag them (only the actual books files) to your Calibre library. If things went right, it should automatically remove the DRM. Confirm that by converting the books to some other format, such as EPUB.
There’s a thing called Epubor, but stay away from it. It’s rubbish.
EDIT: Re-worded one of the paragraphs.
I don’t think KOReader can read DRM protected files.