Hey all,
So… this SEEMS like it should be a simple question, but I’ve been searching for the solution for months on end. Is there ACTUALLY a bluetooth mouse that pairs with a Kindle Fire HD?? I’ve found a zillion different opinions on this one, but there never seems to be a final answer. If somebody knows the mysterious Holy Grail answer, please, PLEASE post it here!! There are virtual chocolate chip cookies in it for you. 
According to Amazon, yes.
http://www.amazon.com/gp/help/customer/display.html?nodeId=201175740
Do you need it to be bluetooth for some reason? Most wireless mice do not use bluetooth, and I think those few that do are significantly more expensive. (I have no idea what the Kindle Fire might support, however.)
The non bluetooth wireless mice generally have a usb dongle that you stick into the computer. The kindle fire HD is not a general purpose computer. It is a tablet and does not have a USB master port so you will not be able to plug in the wireless dongle. Tablets however do generally have bluetooth to connect to these sorts of things.
Amazon sells a Bluetooth keyboard that they specifically mention works with the Kindle Fire HD (the AmazonBasics Bluetooth Keyboard for Android Devices - Black). But they don’t sell a mouse. And the comments in the reviews for some Bluetooth mice mention that they don’t work with the Kindle Fire. Have you called Amazon and asked them?
The kindle fire includes that Mayday thing so you can video conference with amazon support right from the tablet. See if they can give you a good answer.