How to Install Amazon Kindle Cloud Reader App on Ubuntu, Linux Mint & Debian

How to Install PlayOnLinux
Step1 :- Install PlayOnLinux

Download Amazon Kindle For PC (Windows)
Step2 :- wget http://kindleforpc.amazon.com/40514/KindleForPC-installer.exe

Step3 :- Launch PlayOnLinux > Click on Install > Search for Amazon Kindle

Step4 :- Login with your Amazon account

Another Alternative Method

You can go to http://read.amazon.com, sign in and it will download your selected books which you can read in Firefox or Chrome when you're offline.

They've done a pretty decent job on how it works and no installation of extra software is needed.