Our developers have tested it with a couple of Kindle books but there might be some it does not work with. Can you convert the ebooks to txt using this web site https://cloudconvert.com and paste that into the app?
If the Kindle books you have in your library do not contain Digital Rights Management (DRM) from Kindle, then yes, you can import/upload them to Spreeder.
Right now, unfortunately, Amazon will not allow third party apps to access their store or books. Paid books from Amazon are actually DRM protected. DRM protected files are not allowed to be distributed/imported.
There is no sure-fire way to tell if a Kindle book has DRM, though a good rule of thumb is to assume that any book with expired copyright (and available through the Kindle store without charge) does not have DRM, while any book you pay for likely does have DRM.
However, we have prepared a blog post with step by step instructions on how to remove DRM so you can import the books into the software. You can find it here: http://www.spreeder.com/how-to-remove-drm-from-kindle-books-by-pluto-pavlov/