The apps I want to install are not available on the Amazon Market and so I need to sideload them. I enabled sideloading from the settings menu, and then I downloaded the app APK files onto my Kindle.
How do I run APK files that I downloaded onto my Kindle?
As far as i know you should need a simple file explorer, browse to the apk and tap it to run. At least that's how you do it on most Android devices. The kindle fire is one i have yet to play with though, so I might be wrong.