If you are already registered, you can upgrade to CrossOver 23 and Kindle will run fine. But in order to install it in CrossOver 23 you'll need to first install on CrossOver 22 and then import it to CrossOver 23.
You can follow these steps:
Install CrossOver 22.1.1. Here (Linux) and Here (Mac) are instructions on how to keep many CrossOver versions installed.
Install Kindle there.
Register.
Export the bottle as an archive.
Import the archive in CrossOver 23.
Or do it as you feel confortable, the idea is to register first in CrossOver 22, then Kindle will run normally on CrossOver 23
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