I had no luck using bluestacks on both my lenovo tiny pcs. On one bluestacks would freeze, the other the adb backup always failed for some reason I couldn't figure out at returning the file.
I did get it working using nox player (version 7.0.5.8) as the emulator. I didn't have to install adb also as it comes with the install and is in the installed nox/bin directory.
In nox player:
1. I enabled root first from within settings->general
2. I enabled usb debugging for data tfer by going into the tools folder on the main screen. Chose settings and tapped several times on About Tablet to enable developer options. Then back to settings->developer options and enabled USB Debugging.
After this I loaded the Amazon kindle apk - same one mentioned earlier in this thread version 4.16.0.75, then registered with Amazon and sent a book to the reader.
To extract the backup file for the calibre key I went to the nox/bin install directory and ran adb backup com.amazon.kindle from there.
To extract the books I used the adb pull command. I appended the path to where I wanted the books to go to (c:\kindle_books) in my case. Otherwise leave that part out.
adb pull /sdcard/Android/Android/data/com.amazon.kindle c:\kindle_books
This retrieved file tree is what you browse through to import the .prc book(s) into calibre.
I am a novice and would have had zero chance without all the information others have posted here. It was a godsend
So thank you all very much !!! I just made this comment in case it helps someone having no luck with bluestacks.