I was able to set up my other Amazon Fire TV with the Harmony Touch just fine.
All the keys work perfectly on that setup. I added the Flirc device in the Harmony software.
For some reason I can't get my Harmony 700 and the Fire TV to work together properly using the same setup.
Now, I get double-press on the directional buttons.
When I add a random Samsung DVD player everything works except for the double-press on the back button.