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Read the link above. Buy Flirc on Amazon for $30. Follow the guide. The Menu Key is programmed from the command line. If you have an H1, my posted config file might work. My H1 does everything but the microphone as it ain't got one.
I added a USB hub. Have Flirc (a keyboard emulator), an MS Entertainment KB/mouse, and USB stick attached.
Also Droidmote, Play Store, client/server, $3, is a great phone/tablet based remote.
The Harmony One does not do BT. Per Logitech, "Harmony remotes without Harmony Hub cannot control Amazon Fire TV." Are you confusing the H1 with the $300 Ultimate?