just getting for the fist time that there are apps available for a kid .. i was still using the regular versions to teach my niece as well .. but not now as the suggestions are for help in the same matter ..
This can be taken a couple ways, 1) A distro that locks the system down to "protect" the kid from the world (and the system from the kid) or 2) A distro a kid would be able to understand and use.
I bring up this distinction because I think far to many parents these days greatly underestimate what their kids are able to understand and do. For example, I started using computers when I was around 3 I think. I was actually comfortable navigating folders and finding games in DOS before I could even read.
So, my advice would be, grab whatever distro strikes your fancy. Set it up and let them go at it. If you do this on an extra machine you can then let them run wild and learn. They very well might surprise you in how much they pick up. If it is on a extra computer that is just for them to play with then you can just plan on reloading it if they manage to mangle it too badly.
In fact, I would even say, get an extra computer and sit them down and show them how to install it. They might not remember how to do it next time, but at least they will have seen it done once. This is how I learned most of what I know today, when I was young my father showed me how to do things and then turned me loose on the machine.