So this morning I decompiled it and made a few quick changes so it would work better.
The only remaining problem is that I couldn't find out how to reposition the view player (the little tab you can drag up that displays the album art, music controls, etc...). So instead of repositioning it, I moved the music controls above the album art. You can bring it up by clicking the (blank) center button. It works 100%, just doesn't look at nice.
Finally, I replaced the icon with an icon I found in the hi-res folder, so the icon looks all nice and spiffy in the carousel. *You might have to restart your Fire before this will take effect if you have all already installed Spotify on your device*
I attached some picture showing what I've done.
Installation instructions for the plebeians:
*On your Kindle*
1. Go to settings > Device and turn "Allow Installation of Applications" on.
2. Download the attached modified .apk
*For some reason it will give an error if you try to install with the default installer on the Kindle Fire, so you can't simply install it from the browser*
4. Download AndroXplorer for free from the Amazon App Store
5. Open AndroXplorer and browse to /sdcard/Download/
6. Tap KFSpotifyAndroid.apk and it will bring up a dialog asking you to install.
*I lied about being able to install it over your previous spotify app. Make sure to delete any previous Spotify app from your system before installing.*
*This is not a cracked version, simply a small change to the interface, in order to use Spotify on your mobile device you must have a subscription. (Though they do give out trials to new users.)*
And that's that. Enjoy Spotify. Hopefully they're working on a more official version, but this will do until then.