I just wanted to give everyone an update on my fireTV Stick:
At first everything was working ok. I was able to pair my HTC One (M7 - ARHD Rom v81 i think). It was fine browsing menus, but once I opened up Clash of Clans (game) it would disconnect every time. Maybe too much data being sent to the fireTV stick? This was done across 5GHZ and 2.4GHZ N wifi.
I noticed that the Fire Stick dropped my 5GHZ N connection, and went back to 2.4 GHZ without me realizing it. The wifi connection doesnt seem to be very reliable right now. It'll show one connection when its really connected to a different one. The only way to tell is to go into the System -> Network menu. If you just go into the System menu the displayed network may not be correct one as I learned.
Once the Fire Stick dropped my 5GHZ connection it kept acting weird, even after a few hard reboots (disconnecting the power). I got it to connect to my HTC One again, but it took a lot of effort.
Before the connection drop I was able to actually get my SP3 to load the Fire Stick as a projector. It took a bunch of tries while trying to time adding the device at different points of activating the device mirroring on the Fire Stick. At this point I can't get it to find the Fire Stick again.
It looks like something along the lines of the wifi connection and device mirroring is goofing up. Could be a timing issue from what I can tell, but its hard to tell without any debug info. Either way considering my HTC One can't connect reliably (Android 4.4.3), I don't see my SP3 doing any better since it will probably push more data through than my phone.
EDIT: Just wanted to add if you are controlling the fireTV stick from your phone, and activate the mirroring, it will drop the connection it had with your phone.