I have to admit I have no idea how to access it. Nothing jumps out at me when I go to my Amazon Mange Kindle page....
Library loans? Access is through Overdrive equipped libraries. You go to the individual library’s site.
http://www.overdrive.com/News/OverDrive-and-Amazon-launch-Kindle-compatibility-with-Library-eBooks
Overdrive has a search page you can find them on.
Once you’ve checked one out, the library tells Overdrive, which tells Amazon, which then provides the book. Pretty slick!