Fire TV, if it's the same as my Firestick then you won't find a remote under £150 to do that. It's Bluetooth, not infra-red.
I'll post more later.
____________
Devices that use Bluetooth for control won't mate up with regular learning or programmable remotes. They use infrared, so the two systems aren't compatible.
IR needs line of sight to work. That, or it can be used with IR repeaters for when stuff is in a cupboard or in some other way out of sight. Bluetooth can work through cupboard doors or when the remote isn't pointing at the device. The catch though is that BT isn't supported by learning remotes.
Harmony (and some of the high-end home control companies) tackled that by developing a base station that sends out BT signals. In the case of Harmony, it's their £99 Hub.
The Hub is preprogrammed with the individual button codes for devices such as the PS3 and PS4 and a range of the Amazon Fire products. It also acts as an IR repeater. What happens then is certain Harmony remote with a built-in wireless function can link to the Hub, so you press a button and, depending on the device being controlled, the hub sends out either IR or BT signals.
So far so good.
Harmony remotes with this wireless link facility start off with the basic button-only Companion @ £70, and go up to the touch screen Harmony 950 @ £180. Those are the discounted prices on Amazon. Add them to the discounted price of the Hub @ £80.
Potentially then, for £150 with the Companion and Hub, your remote can control the Fire TV. What they don't mention is that you'll need to set this up before it will actually do anything.
Now, before I continue, I'm going to put my cards on the table as a AV dealer and a user of AV gear in my own home. I saw Harmony at a trade show back in 2001 or 2002. At the time the company was just getting off the ground. The basic ideas were there: a handset that links to a computer for programming, and a comprehensive code base, and some online assistance to patch things when codes or functions were missing. The code base and the online patching were the two big differences to the main competitors in the market.
With something like a Philips or Marantz touchscreen, you built everything from scratch. Codes were learned directly from the source remotes, and with the PC program you'd set up the flow of the remote and what buttons were on which screens and how it responded. It was very much a blank canvas and a bit of a steep learning curve for novice users.
Harmony promised to make things far simpler, and I loved that idea because one of the big stumbling blocks for guys with families trying to get in to DVD and surround and home projection was always how many remotes were required. Wives hated that money was being spent on stuff that often they couldn't use. What was even better about Harmony was the price. It was less than a quarter of the cost of a Pronto 890 or Marantz RC5000.
Coming back to getting a Harmony up and running with the Hub...
There's going to be some physical set-up which is mostly going to be you fiddling with the position of the Hub itself so that IR hits the devices that need it. Then there's going to be the bit of set-up using a computer and Harmony's online wizard program to tell the remote what devices you have.
This might sound like a daunting task, but plenty of folk have bought Harmony remotes and done this, so it's not a huge deal in itself. Here though is where the user experience starts to polarise in to two camps.
In one camp you have the people who have never had a proper system remote. They're impressed that one button starts their system, and that another couple of presses turns some device off and switches another on so they've now changed an activity. These are very simple command strings called macros. You do more or less the same when you switch the TV from viewing say Freeview to the Fire TV. That's all a macro really is.
The people in the 'I love Harmony' camp tend to be relatively easy to please because their needs are fairly simple, or they're happy to accept the way that Harmony does things, and they don't mind then pecking at the buttons to find where Harmony has put some function that they use regularly but the Harmony designers have buried. They've never seen or used a proper bespoke touchscreen remote to know that things could be a lot better.
This brings us to the people in the "I hate Harmony" camp.
They tend to be the people who have some IT experience or, maybe because of their job, they've used something at work or during professional presentations that controls a whole bunch of AV gear and the lighting and the air-con and the video conferencing and... and... and. I'm sure you get the picture. The point is that when they sit down to program a Harmony, they instantly recognise how dumbed-down and restrictive the wizards and online programming is.
Simple stuff such as arranging a button layout on a screen is impossible. Say you have a sound system, and from time to time you'd like to change the surround sound mode from within the screen you're using to control the TV. The wizard doesn't want you to do that, so you end up with the remote where you have to change devices (the equivalent of picking up another remote) just to change an audio setting.
There are other annoying traits such as the remote's insistence on turning things off when moving to a new activity. Anyone with a Sky box shared around the house will have come a cropper on that one. That brings us to the power toggle issue where some device that was already on gets switched off as the system starts up.
Then there are the creature comfort issues. The remotes are black and the button text is small and unilluminated; and there are a hell of a lot of buttons. Also, the display screen is fairly small and there's no easy way to make the icons and text any larger. If you're getting on or need glasses for close-up reading, then just doing something simple might well involve putting a light on and donning some spectacles.
Due to a career change, it was probably about three or four years later before I got my hands on a Harmony. I'd just installed a projector in a customer's home when they came and asked if I could help them set up their Harmony. By this time I was already doing some quite advanced programming on Prontos, so I thought that the Harmony would be a doddle.
O....M....G. How wrong was I?
I understood instantly why Harmony isn't aimed at the AV Installer crowd. It's just too limited. It's a end-user DIY install product because, in a lot of cases, these customers will give in when confronted with the difficulty of tailoring the remote to do what they want.