Since shooter is available on the Amazon App Store you should have no problems with it working on the Kindle Fire.
However the Kindle Fire doesn't have bluetooth so you couldn't connect it to a Kestrel
BT model. It also doesn't have a GPS chip in in so you couldn't use it for any navigation stuff. Also somewhat limited on space.
I am planning on using my Acer Iconia A500 for Shooter and GPS stuff on trips, a bit heavier and bigger but is has GPS and bluetooth in it, and about the same battery life. You can even get USGS maps as PDFs and keep them on any of these tablets too. Might save on some space. As long as you are conservative with the battery and remember to turn the wireless off when you are not using it it should be pretty good.
I know there have been a lot of solar chargers making their way on to the market lately as well. I am definitely going to look for one for my tablet. I know there is a lot that could go wrong with electronics but I love mine and they are what I do so I am going to see what I can do with them.