Recently we bought Kindle Fires for all the boys.  A lot of reading about this issue led me to the conclusion that if children are given unlimited access to electronic media they will initially spend all their time on it, then move on to other things and treat it like any other toy.  We have configured them so that they cannot watch tv programs on them, and of course we decide what can and cannot be downloaded.
Their favourite app so far is Minecraft.  Although I don't play it myself, it is a building, creating, Lego type game, and we have it set up so that they can play together.  Frequently they are all sitting on the lovesac together, on their own Kindle, playing together, talking together and working together.  This is no different from a board or card game.  For the most part there is far less arguing than normal between the 3 of them, and I leave them to it.
They also like to browse the app store and look for new apps.  If they can afford it, and the game looks suitable, I download it for them.  They have got very good at seeing how much they cost (or whether they are free), and most importantly how they have been rated by other users.  Several apps have been decided against when they see the poor ratings. This is a really good for decision making processes.

I have never worried about Edward using a Kindle.  He so enjoys making things that I knew he would not spend all his time on it. He downloaded an app that prints out patterns for making the characters in Minecraft.  He quickly worked out how to make the patterns himself and has been busy making them.  He also used actual Lego to build the sets in minecraft.  On another game, hunting for prehistoric animals, he knows all the animals and we have looked them up on Google and had great discussions about them: herbivores, omnivores, size, weights, how they compare with modern animals....

Philip enjoys playing Minecraft, especially with dad.  However, he is more than happy to put it down to go out and play with friends, fishing, learning to walk on stilts, lacrosse, etc.  I often read to them in the afternoon and he loves listening to the story and usually puts away his Kindle.  His ability to track with a book which I think is above his head is impressive, and his working vocabulary is way ahead of an average (nearly) 7 year old.

Benjamin has been my biggest worry with the Kindle, as he is likely to be the biggest couch potato and watch tv all day if he could.  However, he is playing games well with his brothers and goes on to other things quite easily.  I would say that he is generally happier and we are not arguing about screen time any more. He also likes to listen to stories and is the first to put away his Kindle in favour of stories.

Overall, I am happy with the decision to buy them their own Kindles.