Here is the latest version (9.3.2) for the Kindle FireHD 8.9 as of a couple of days ago.
Clicking on the graphic will take you to a download site in the cloud.
NOTE: The file was taken off dropbox. I am not sure why. It is a free browser. Get it here, http://ourexcellentadventures.com/wp-content/assets/Dolphin_HD_9_3_2.apk
This browser works on the Kindle FireHD 8.9. It has not been tested on any other type of Kindle. Flash works with this browser.