1. Make sure your Kindle Fire has been configured to allow installation of third-party applications. Tap the Quick Settings icon, tap 'More...' then tap 'Device'.
2. Go to 'Allow Installation of Applications' and move the adjustment slider from 'OFF' to 'ON'.
3. Now you need to locate your Android app to download. Go to the website of the app you are interested in and save the Android APK file (remember you are getting this .apk file from the developer’s site, outside of the Amazon Store) and save it on your computer. You just saved the APK file to your hard drive, and then connect the Kindle Fire to your computer (PC or Mac) using a USB cable. Copy the download APK file into the Kindle Fire Download folder, and then disconnect the Kindle.
You can also download the APK file directly to your Kindle Fire if you know the URL of the app. In this case, you just wait until the download is finished and tap the notification icon in the top left corner of your screen to begin the installation process.
Use the ES File Explorer app (available for free at the Amazon App Store) to locate APK file(s) that you copied onto your Kindle Fire /Download folder. Go to the Home Screen of your Kindle Fire and tap on the Download folder: