Children respond wonderfully to Reiki as it is so gentle and "magical".
In my experience, children will feel the Reiki flowing far more quickly than adults seem to. It is almost as if they are "ready tuned", which in a sense they are. They have no pre-conceptions to unlearn and hence will accept whatever they feel as perfectly normal and natural.
Depending on the age of the child a Reiki session should last between 25 and 45 minutes. The timing is really dependant on Reiki itself and the reaction of the child, both to the warmth of the energy and to the amount of time they are able to keep still!
Naturally, parents are always present when children are being treated, unless they elect not to be. I make no claims regarding treatments, but I can share my experiences with you, and I have found that Reiki is particularly beneficial to "Hyperactive" children, those who have difficulty concentrating, and of course children who are in pain, for whatever reason.
Their innocence chimes so well with Angelic Reiki that this is the form I tend to use with them. If you do decide to bring your child for Reiki and they tell you that they saw an Angel, all I would ask is that you believe them!