I have a few books I've bought for reading using the Kindle app on my iPhone. I'd like to be able to read them on my Fedora Linux based MacBook as well, but Amazon hasn't released a version for Linux yet, which is ironic given that the Kindle's OS is Linux based. All is not lost, there is an excellent project called Wine that enables you to run many Windows applications on your Linux system. My experience with it has been mixed, with some applications working fine and others not making it past the installer stage.
The trick to get this to work is to use the Beta version of the Kindle for PC app. Specifically this version - 'Kindle App v1.0 Beta 1 (25338)' The sha256sum for the .exe is 83f1190a7f4a914921d17546d6fe8f9ba609275b4af0fa5619398b87643a2779 and it is currently available from here as a .tar file (the .exe is inside the .tar).
My setup is pretty simple, install Wine from the Fedora repository and make sure SELinux is set to permissive. I do enough different stuff on this machine that leaving SELinux enabled always ends up causing more trouble than it's worth. Download the Kindle app installer and double click on the .exe, this will run the installer and prompt you to enter your Amazon login info. It will create a launcher icon on your desktop for easy access. That's all there is to it!
Thanks to Greg Laden for his post on how to get this working. With Fedora 13 I didn't need to set it to run as Windows 98, leaving the defaults worked fine.