I picked up a Fire TV HDMI stick during last week’s Amazon Prime Day and the built in streaming/casting wasn’t working with my Nexus 6. It turns out the Nexus 6 doesn’t have miracast enabled by default, but it can be enabled in the android build.prop file.
To enable miracast you must be root. You can then edit /system/build.prop using either a text editor or a build.prop editor app. Add persist.debug.wfd.enable=1 and you should then be able to cast to the Fire TV.
Now I just need to figure out how to enable the Fire TV to always listen like a Chromecast instead of having to manually enable screen mirroring every time.