The Short Method:
- Tap on the icon in the top-right corner that resembles a sprocket (or snowflake, if you prefer).
- Tap More.
- Tap Device.
- Tap to change "Allow Installation of Applications From Unknown Sources" from off to on.
- Open your browser and navigate to http://www.2shared.com/file/uyovLzoz/Spotify-41200180.html
- Download the Spotify APK file
- Tap the number in the top to bring down a window showing completed tasks
- Tap the Spotify APK file and follow the instructions.
- Log in and enjoy Spotify.
If you would rather get the Spotify APK yourself, here are the instructions for creating the backup from an existing Android installation, such as your phone or other tablet with access to the Android Market:
- Download and install Astro File Manager from the market.
- Download and install Spotify
- Open Astro File Manager and choose "Application Backup."
- Scroll to find Spotify and tap to select it.
- Tap Backup.
- Open your preferred email app and compose an email to yourself to an account you have setup on your kindle.
- Attach the spotify APK file that was generated. It is in /mnt/sdcard/backups/apps
- Send it to your email.
- Download the attachment and install.
Incidentally, the above method for creating APK files will work for any app in the Android market that you did not have to actually pay money for, so if there is anything else in the app store you want, there's a good way to get it.