I thought the Kindles used 3G radios (that piggyback on Sprint)... <googlie-goo>
Shows how up on these things I am - they dropped Sprint in 2009.
http://www.amazon.co...let/dp/B0083Q04IQ (scrolldown) has a big table of features, etc.
If the issue is connecting to a network, and 3G being better, then the Fire won't help much (unless you get the $500 one with 4G). If the issue is the Kindle he has doesn't do enough, then the Fire would be a better fit if he is a fan of Amazon and what it offers.
The Fire is basically an Amazon-consumption device.
Does he want to read with it, watch movies, play games, something else? Just something to play with to keep up with the world outside? Are you worried about him accidentally buying lots of movies or games?
Unfortunately, these things that require access to a "store" for updates, etc., are dangerous if you're not as sharp as you used to be. It's very easy to spend lots of money without thinking about it.
I finally had to give up on the idea of a tablet or smart phone for my mom. She's 75 and had a pretty bad stroke a few years ago, so has many physical issues. I think it would help her to stay active and sharp to have something that would keep her occupied (other than watching TV all day), but she doesn't have the dexterity to keep it charged or be able to handle and use it. So, unfortunately, it isn't going to be. I'm sure your FIL isn't in that situation, but don't forget that these things are complex machines and can be frustrating to use without lots of hand-holding at the beginning.
Is an iPad mini an option? Or a used iPad? You can't beat that ecosystem for content right now, and the UI is very well done. It means iTunes and the Apple App store, of course, but such is life.
HTH a little. Good luck.
Cheers,
Scott.