Amazon's Kindle for Android application uses an internal key equivalent to an eInk Kindle's serial number. Extracting that key is a little tricky, but worth it, as it then allows the DRM to be removed from any Kindle ebooks that have been downloaded to that Android device.
Please note that it is not currently known whether the same applies to the Kindle application on the Kindle Fire and Fire HD.
Obtain and install adb (Android Debug Bridge) on your computer. Details of how to do this are beyond the scope of this help file, but there are plenty of on-line guides.
Enable developer mode on your Android device. Again, look for an on-line guide for your device.
Once you have adb installed and your device in developer mode, connect your device to your computer with a USB cable and then open up a command line (Terminal on Mac OS X and cmd.exe on Windows) and enter "adb backup com.amazon.kindle" (without the quotation marks!) and press return. A file "backup.ab" should be created in your home directory.
On the right-hand side of the plugin’s customization dialog, you will see a button with an icon that looks like a green plus sign (+). Clicking this button will open a new dialog with two main controls.
Click the OK button to store the Kindle for Android key for the current list of Kindle for Android keys. Or click Cancel if you don’t want to store the key.
New keys are checked against the current list of keys before being added, and duplicates are discarded.
On the right-hand side of the plugin’s customization dialog, you will see a button with an icon that looks like a red "X". Clicking this button will delete the highlighted key in the list. You will be prompted once to be sure that’s what you truly mean to do. Once gone, it’s permanently gone.
On the right-hand side of the plugin’s customization dialog, you will see a button with an icon that looks like a sheet of paper. Clicking this button will prompt you to enter a new name for the highlighted key in the list. Enter the new name for the key and click the OK button to use the new name, or Cancel to revert to the old name.
On the right-hand side of the plugin’s customization dialog, you will see a button with an icon that looks like a computer’s hard-drive. Use this button to export the highlighted key to a file (with a ‘.k4a' file name extension). Used for backup purposes or to migrate key data to other computers/calibre installations. The dialog will prompt you for a place to save the file.
At the bottom-left of the plugin’s customization dialog, you will see a button labeled "Import Existing Keyfiles". Use this button to import any ‘.k4a’ file you obtained by using the androidkindlekey.py script manually, or by exporting from another copy of calibre.