What part of Kindle? The physical ebook reader device, the book store, or just software to read ebooks?
There's plenty of the latter in the open source space; with any standard GNU/Linux installed on any kind of device, you could have a folder on disk full of .pdf or .epub or whatever files and read them with the likes of GNOME Books or Foliate.
I've seen some raspberry pi projects people had built with an e-ink display if you want a physical reader running free software, there may be some easier options for that, or get any tablet computer capable of running Linux on it (MS Surface Pro, etc.); if you want the Kindle book store or things that get closer and closer to Amazon's proprietary products, you'll likely not find much luck there.