I have written several articles lately about new genealogy apps for Android devices. The most recent article was RootsMagic for Android is now Available at http://goo.gl/WY2YkZ. A common question asked after each article is published is, "How can I intall this Android app on my Kindle Fire tablet?"
The Kindle tablets are produced and sold by Amazon and run the Android operating system. However, when first unpacked, a Kindle can only download apps from the Amazon's Kindle App Store, not from the bigger collection available in the Google Play Store. Many Kindle owners discover there are even more apps available Google Play Store for Android devices but those apps remain unavailable to Kindle users unless they take "extra steps" to use the Google Play Store. The "missing apps" in the Kindle App Store include several genealogy apps.
GizMag.com has a one-year-old article that describes how Kindle users view and download apps in the Google Play Store. One warning, however: the article clearly states, "...it will instantly void your warranty with Amazon." If you don't mind losing your warranty, you can read the instructions at http://goo.gl/dF7fKM.
If you don't want to void the warranty, a new article by Brian Burgess on GizMag.com explains how to "sideload" Android apps onto a Kindle Fire in such a manner that the warranty will remain in effect. However, it does state that it will work with most of the Google apps. You can find the newer article at http://goo.gl/WSkG5d.
Disclaimer: I don't have a Kindle Fire so I haven't tested either of these methods. If you do have questions, I suggest you ask in a comment at the end of the appropriate article on GizMag.com.