So here is how i have fire tv setup with my flirc.
I'm using the harmony smart control for everything:
It supports fire tv out of the box (the hub does RF/IR/BT) and you pair it with the fire tv as a bluetooth controller (not a remote).
That gets me all the functionality of the basic little fire tv remote. It's enough to get by with kodi but I wanted more functions so in comes the flirc.
First, you take the flirc, install the pc software, plug it in, update the firmware.
At this point you can map any IR command to a keyboard shortcut. But since I'm using a harmony I can skip that step b/c on the harmony you can add the flirc as a device:
So now I go customize the buttons on my "watch fire tv" activity on the harmony, map a bunch of flirc/xbmc device functions to all the buttons that the default fire tv remote doesn't use (or long presses, etc) and I have a really nice integration of native fire tv remote commands over the hub -> BT fire tv and auxiliary xbmc commands through hub -> IR flirc -> fire tv.
Lets take another scenario where you just want to use some random IR remote for fire tv / kodi.
In that case you would need to have the flirc LEARN each button press and map those to keyboard shortcuts using the flirc pc software. Then you should be able to use that IR remote for controlling everything on the fire tv.
Fire TV is now enduring WAF trials and stability testing but so far so good.