Use Zotero to grab the citation/bibliographic information from Amazon, or better, a library catalog (which will have a fuller citation with added information).
The actual Kindle book cannot go into Zotero (DRM/incompatible formats), and you wouldn't want it to anyway because it would eat up space.
It's easy and painless to move the highlights and notes you made while reading the Kindle book into Zotero by copying and pasting the "highlighted passages" in "your books" at Amazon into the Notes field of the Zotero citation.
Directions: Managing Kindle Highlights and Notes in Zotero