Not seemlessly because Amazon has their store locked down to Kindle. But you can export all your books from the Amazon web interface or use the desktop Kindle app to download them all. You would then use Calibre with a couple plugins to deDRM them. At that point you have plain ebook files in Amazon's format to do what you want with. Calibre can convert them to any one of the open ebook formats (I personally prefer epub) and sync them to your device(s)). Those ebooks are treated like any others and fully supported by PocketBook cloud if you use it. The convenience of Amazon's store for Kindle is nice, but it's also how they lock you in to their ecosystem and devices so you keep only buying/paying for a subscription with them.
The process is really not bad at all if you use the desktop Kindle app to download your library before importing to Calibre. Each step is fully automated with the only manual parts being setting it up and doing each step in sequence for the whole library but not each individual book.
I haven't been able to find any sort of option to export from the web interface, and poking around at it with dev tools I don't see a non-trivial way to grab whole books. Am I missing something obvious?
The process is really not bad at all if you use the desktop Kindle app to download your library before importing to Calibre. Each step is fully automated with the only manual parts being setting it up and doing each step in sequence for the whole library but not each individual book.