How to install Android Apps in Your Kindle Fire HD without Rooting?
Go to Menu bar >> More >> Device >> Allow installation of application.
You get a warning for using applications from unknown sources, your kindle and personal data are less secure and there is a risk of unexpected behavior. Ignore it, simply click OK to proceed
Now, try installing an app, using APK file.
From your Silk internet browser Download Astro File Manager APK file for your Amazon Kindle Fire HD, direct APK file link here: