Instagram for the Kindle Fire HDX
1. Go to ‘Settings’ and click on ‘Security’.
2. Make sure ‘Apps from Unknown Sources’ is ‘On’.
3. On your Kindle Fire, go to the default web browser and go here to download Instagram .APK file:
Instagram .APK
4. After the file is done downloading, go to the menu icon and click on ‘Downloads’ and install the .APK file.