I'm writing this in the Blogger app on my Kindle Fire because I can :-).
I used the How to Geek guide for this. I'm not going to duplicate their content here, but I am linking to them to help people find their useful guide and telling you how it varies slightly for Windows 10.
When following the above instructions on Windows 10, I stumbled at the second part, 'Install the ADB Drivers'. I tried a few things, but I could not get them to install. A few people had posted similar issues in the discussion section, but I didn't see any solutions. Perhaps that's because the solution is so simple; just skip that section :-). It worked for me anyway.
So here is what you have to do:
Go to Installing the Google Play Store on Kindle Fire HD.
Follow 'Preparing Your Fire'.
Follow 'Download and Run the Script'.
Enjoy loads of Android apps previously unavailable to you.
Obviously you do this at your own risk and should back up your device first! Just because this worked for me, doesn't mean it will definitely work for you.