You install the APK via a USB stick or memory card. I posted the first link that I came across and haven't had time to read it fully.
I have never owned a Fire tablet but with my Amazon firestick, I had to change the settings to allow me to sideload (read: install something from somewhere than the device approved app store).
Amazon Fire tablets have a lot to offer, but there’s one big catch. The Appstore has far fewer apps and games than you can get on an iPad or from the Google Play Store. Thankfully, we can solve that problem.