With well over 2000 views, there is apparently a lot of interest in this topic. Obviously no one wants to invest in another $300.00 remote control with a unifying "hub" if they don't have to. I have the original Harmony One and I was loath to give it up as, IMHO, none of its successors has duplicated the button placement, touch screen placement, and usability of that unit. If other peripherals start to make use of Bluetooth remotes it might be necessary to bite that bullet, but not yet.
It has taken a lot of digging and reading of other threads here at Flirc to verify, some of them going back two years, but the statement made by Dave_O a few posts up is true. I can't speak for that particular OTG dongle he links, as I purchased a different but similar one. But if you have the new V2 Fire stick, you can use the Flirc USB to program your IR remote to control it, and connect it with an OTG dongle. Getting it to work perfectly with all the Fire TV apps, including those that have to be side loaded, can be a challenge, but it can be done. Unfortunately, from what I read, the original Fire stick's USB port cannot be used for anything other than a power source, so this only applies to V2.
Here's a short tutorial. Any references to procedures that work with the Fire TV box should also work with the stick as of V2. Jason Kotzin is the go to guy, although he is probably not too popular at Logitech :-)
And for the historical process that got Flirc to the software version of today, which was not easy, some light reading: