Originally Posted by DoctorOhh
It may or may not run on the Fire HD, but currently Calibre Companion is only available from Google Play store. Additionally if the owner of the Fire HD managed to download from Google play to their Fire HD it may not (like other Android devices) be able to launch books directly into the Kindle app since on other Android devices it does not expose itself as a reader for any format. Most likely, as with other devices, the books would have to be directed to the correct directory and opened from within the Kindle App.
In theory any android v2.3 or higher. I know folks have run it on their rooted Nook Color ereaders. (Ooops I guess Nook Color isn't eInk)
@DoctorOhh, thanks for the info. (It would be nice to combine the best of both worlds: Calibre Companion and e-ink reading device. If it were possible.)