I think you could find chickens in most any breed that will do well with kids, although there is also a bad chicken in most every breed as well. The most common 'friendly' chickens that I know of are buff orpington and silkies.
From a personal perspective, we raise several different breeds, so I'll give you some insight on those.
Our buff orpingtons are what I call my gentle giants. They are large fowl (also available in bantam, but tough to find) and all of my hens and roosters are gentle. The majority of this group are tame and will eat out of your hands and let you pick them up.
Our Easter Eggers are a little more flighty and not so quick to greet you. There are a few girls in that flock that appreciate a cuddle and like to see you come out for a visit. Don't get me wrong, the others will come for a snack, but otherwise, don't really want to be bothered. The rooster does his own thing and is not really bothered by us. He takes good care of his girls and that's what he is here for. Our other rooster we had in that group, was a big meanie and attacked every chance he had. Don't know why...he just had a mean streak in him. They are certainly not all like that.
Our Araucana is another large flock here and we have mixed personalities there. All of our birds do well with adults, but there is one rooster that scares my daughter. I don't think he means harm, but he does act a bit intimidating towards her. He's on the small side and spunky, but by no means aggressive. We also have wonderful roosters that like to sit on your lap and snuggle or just like to see what you're up to. The hens are fairly different as well...some like company and others are saying 'hey, get out of here...this is my space".
Our silkies are a lot of fun and from the short time I've had them, I've found them to be very mellow. They don't mind a hug when you want one and they love to see you for snacks. They seem a bit shy to me, but maybe they'll loosen up in time. I can pet all of them without worries and my daughter loves them.
Now, having said all that...you can get very mixed results and for various reasons, regardless of the breed you choose. A lot depends on how you raise them and who does a lot of the handling and caring for them. While most tameness comes from a lot of handling and interaction, there are exceptions as you can see in my notes above. An individual chicken personality does not speak for the whole breed, so what one of us experienced with one or many birds, you could get completely different results. I hope this is helpful and wish you the best in your choice.
Jody
