The test results you have selected are very old and may not represent the current state of Wine.
Selected Test Results (selected in 'Test Results' table below)
Downloading and reading books.
What does not
"Shop in the Kindle store" didn't work. It would only search the titles I had already downloaded.
"Recommended for you" opens in Chrome instead of default Iceweasel.
What was not tested
"Manage your Kindle" as I don't own one.
Failed to install until I removed ~/.wine/drive_c/windows/winsxs/manifests/x86_microsoft.vc90.crt_1fc8b3b9a1e18e3b_9.0.30729.4148_none_deadbeef.manifest.
After the install the program auto-ran. Upon entering my Amazon account info, I found I had 3 PD books installed. I added 96 free books to give it a test run. Nice fonts. Smooth scrolling.