Well, thanks to this thread, I found that my Kindle FireHD 9.8 works just fine with CC and I've loaded it up on that, the 7" HD, and my wife's 8.9" HDX. Now, if I really want to take the wireless full circle, I can run Calibre as a terminal server RemoteApp from my Kindle FireHD, connect it wirelessly to that same Kindle FireHD with CC, and Send To Device from the RemoteApp session. All without getting off the Chesterfield.
