I just picked up a Fire TV over the weekend, and have installed KODI onto it.
Note, I've been running KODI on an Intel NUC with built in IR, and controlling it with my Harmony One for over a year.
Now, with the Fire TV, I'm using the FLIRC (v1.36) with my Harmony One.
I've managed to get all the basic functions setup with the FLIRC, so the Fire TV & KODI control buttons work on the H One.
The one thing I've been having a problem with, is that on the One, when I use my Intel Nuc, I have 2 LCD buttons at the top Update Library, and Clean Library.
I set these up on the Nuc according to the guide here: http://wiki.openelec.tv/index.php/Config_harmony
Now, on the FireTV/KODI installation, I've copied over the keymap.xml from the NUC to the FireTV (rebooted, etc).
But, when I press the button to update or clean, in the harmony profile for the Fire TV, it doesn't do either function.
I tried to map the #1 key on the full keyboard in the FLIRC to the 1 button on the Harmony, but that didn't seem to help. Also tried mapping 1 & 2 in the KODI controller in FLIRC. The keymap.xml file sets key 1 and 2 to do the update and clean.
I'm not sure what I'm missing, but needed some assistance.