How to copy and install apk files to your Kindle Fire HD
Copying Android files to your kindle manually
There are a couple of ways to install apps on your Kindle fire hd with the primary one being using Amazon's own apps website when you go to apps from your home page link. You can however also install apps by going to third party sites like apps.opera.com and others that offer Android files. You should however note that Amazon doesn't recommend installing such .apk files from third party sites since she can't vouch for their security and that's why by default, you can's install .apk files to your Kindle without having to adjust the app installation settings.
Allowing installation of Android files from Non-Amazon sites
This is mostly useful for people who use Kindle fire HD outside the USA, in countries in Africa like Nigeria, where Amazon doesn't offer much support for apps apart from offering their silk browser. You will need to first go to settings > Device and Switch the Allow installation of applications (From unknown sources) on
Once, you've enabled installation from such third parties, you will be able to make further installations of apps outside the Amazon store as well as by copying from your computer to the Kindle hard drive.
Downloading and Copying .apk files to Kindle
When it comes to downloading apps for Kindle Fire HD, you'd need to make use of an android device like Amazon's silk browser or Google Chrome. With Google chrome, you can go to Android supported sites like apps.opera.com and download a lot of .apk files which you can later copy to Kindle for forward installation. You can download a lot of files and then copy it to your Documents folder in Kindle for later installation. Google Chrome is an android browser such as Silk browser and they work almost the same way as far as I know.
Once you've downloaded the games or apps you want to copy to Kindle fire hd, you can then connect your Kindle fire hd to the computer using a USB cable and then save the files in your Documents.
Can't see the copied .apk file in Kindle storage?
If you've already copied the .apk files to your Kindle's internal storage and still unable to see the file after making use of your office suite in the apps folder for browsing, then you probably need to install an explorer app called ES File explorer. The app will enable you to view those files which Kindle's office suite does not allow you to see just because they didn't come from Amazon's trusted sites. First of all, you should use your Kindle's silk browser and go to apps.opera.com and install the ES file explorer. After installing it, you will then be able to view any other files you've copied to Kindle storage and be able to install .apk files too just by opening them.
How to install copied .apk files in Kindle
You can now start copying a lot of .apk files to your Kindle but make sure that they come from trusted third parties if not from the Amazon store. You can simply copy them to Kindle documents after downloading it with Google chrome on your computer. Once copied, you'd be able to view them by simply opening your ES explorer or any other app that allows you to view them. When you open them, accept the installation prompt and it would be installed on your Kindle Fire HD.
Hope this helps. I had been battling with it for a while until I found out I could just copy Android apps from my computer to Kindle and install them easily.
Getting apps from the Amazon store
The Amazon app store also does have a wide range of free apps you can easily install on Kindle but if you are unable to install them from your location, you can always visit the Opera apps store.
If you have got access to the Amazon store, you can get a lot of Android apk file there suited for the Kindle device. It is probably the best place to get most of the latest apps and games suited for Kindle Fire. Some come for free while others would require some form of payment.