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Everything works like a charm
What does not
What was not tested
I only did a cursory test, but my results agree with the other few testers.
Originally, the installer ran, but the application would not display, and gave no error.
The key was to 'export WINEPREFIX=~/.wine/kindle'. This gives it a fresh new wine area to install to. I notice that the launcher icons preserve this setting, so you won't have to worry about it again (they prepend a 'env WINEPREFIX=blah', so that this piece of environment is always set).
I saw a lot of advice recommending to remove the .wine directory to start fresh, but it's not necessary, and I have a good number of wine apps that I didn't want to reinstall.