Note: This tip applies to CrossOver 9 only in CrossOver 10 and over use winxp bottle, and it is always better use the crosstie way.
Win98 is the only working bottle at the moment- any other bottle will fail to render fonts. I'm still working on figuring that out, but for the moment, use Win98.
To install using the win98 bottle, just install the core fonts and Internet Explorer 6. At that point, you'll be fine installing Kindle for PC.
You'll also want to update the font resolution (thanks to Don for the tip!). After installation, run cxsetup and select the Win98 bottle you used to install Kindle. Click Configure => Control Panel => winecfg. Once in WineCfg, click the "Graphics" tab and adjust the Fonts DPI to something higher than 118. I was happy with 118, you can adjust to taste.
Again, thanks to Don for the tip on fonts!
Good luck, post if there are any difficulties!