So, the latest version of Amazon Kindle for PC sort of works when using the latest CrossOver. I'll explain.
After a successful install, the application will open, but part of it will crash, resulting in this error. Installing Visual Studio 13's Visual C++ Redistributable does not seem to solve the problem.
Anyway, you can close this error box, and continue using the application, which ranges from 'it's working!' to 'Wat?' You see, there are some books which, when you attempt to download them, seem to take forever to transfer over...and even at 100%, they don't appear in your Downloaded Library area. Closing the app, and reopening it does not make these 100% downloaded but not officially counted books appear as part of your library, but instead makes it treat your book like an unsaved download (making all that progress disappear into the void); fun times. Oh, and it's not all books, just some of them -> in my case, one example is the "Compendium Maleficarum."
Test Platform: Linux Mint 18, Toshiba Satellite w/ i7, 16GB RAM, (and so on-in other words, all the fruit, or a typical developer's laptop)