http://bugs.winehq.org/show_bug.cgi?id=36799
--- Comment #1 from Rosanne DiMesio dimesio@earthlink.net --- Upgrade your version of Kindle for PC. I remember last year getting messages from Kindle when I started it to the effect that the version I had was expiring by a certain date and I needed to upgrade. After the expiration date, without upgrading, the app would just shut down on start. Upgrading fixed it.
I have 1.10.8 and it's working. If upgrading the fixes it for you, then this bug is invalid.