Have you found a kindle fire screen cover that actually works? I have purchased one that still leaves me with fingerprints & smudges.
Actually I do NOT like covering my gorgeous screen on my Kindle Fire at all. The glass on this marvelous device is very special and when taken proper care of, really won't smudge much at all...
I keep an eyeglass cleaning cloth (if you wear glasses you know what I mean) tucked into the Oberon leather cover that houses my Kindle fire. It is unobtrusive and nice and handy for a quick wipe down whenever I use it (I hate fingerprints too). Recently I discovered a little thing that works great on the screen and even keeps fingerprints at bay longer than I would have thought. It is a lens cleaning pen I had lying around for my Nikon camera. Just for giggles one day I tried it out on my iPhone and was amazed at the results. I did a little more research (on Amazon of course) and discovered the same company even makes a larger version for the iPad screen, which means it also works great on our Kindle Fire screens.
The LensPen Sidekick is a great tool, and small enough to keep close at all times. You can get over 300 uses out of the thing (it says on the container) and it isn't messy. It just feels good for the screen too... seriously, if it is good enough for a Nikon lens, it is good enough for my Kindle Fire or iPhone screen.
I keep the original LensPen in my purse so it is always handy for my iPhone, and even have been known to use it on my reading glasses... It is amazing!
You mentioned your screen cover had fingerprints too... I think you will find this will be much better. It seems to give the screen an invisible coating that actually repels those pesky fingerprints (I have no idea how), and you will be able to really enjoy your screen the way you should.