Today's Free App of the Day is ShisenSho
Originally $1.99

Nine reviews, five of them four stars and above, though at least one of the five star reviews appears to be bogus (Steve) based on my research. I've test driven this one, and frankly I don't recommend it. It's got some non-standard Mahjong rules which are confusing initially, the highlight for available moves is not consistently correct, the whole screen rewrote once in blank tiles. Now, granted, these could be artifacts of the "test drive," but, even free, I wasn't encouraged to try it given the test drive experience combined with the reviews.

So, we have a KBAAD (and a bonus KBAAD)--two well reviewed Mahjong games. I have both of these. I got this one last year, it has great reviews:

Mahjong Deluxe HD Free (579 reviews, 447 four stars and above)

And, in honor of the season, a bonus KBAAD:
Thanksgiving Mahjong (52 of 60 reviews four stars and above)

Note that if you check out the Free App of the Day on your Kindle Fire, at least on the Fire HD8.9 (Apps tab > Store; the Free App will be the first one in the banner), there will often be a test drive button right on the App product page. It'll be a green button right below the orange purchase button on the left side of the page.

These apps are compatible with the original Fire and works on my Fire HD8.9. To tell if an app works for your Fire HD or other Android device registered to your Amazon account, click on the above link and look on the right side of the web page. Amazon will tell you if it will work with your registered device.

Have fun!