Hi. Our 3 year old son had kawasaki disease in sept 2012. He complains a lot with pain at back of knees and his back. Could he have arthritis?

Likely not. Kawasaki's disease is an inflammatory disorder, and can have a number of issues, but long term arthritis is not really one of them. There can be inflammation for other reasons that may be related, so if the pain is continuing, he should be re evaluated and a thorough exam done.
Who follows him? Some children with kawasakis have some arthralgias (joint pain) diagnosed around the same time. I have seen it linger in some. This is often treated in a fairly straightforward way. Have the doctor who is following him up for the kawasakis evaluate him.
It's possible. . According to the arthritis foundation, kawasaki disease is one of over 100 types of arthritis. Arthritis or arthralgia can occur in the first week of the illness and tends to involve multiple joints, including the small joints as well as large weight-bearing joints. Sometimes back pain in children could be related to low vitamin d levels. Vitamin d blood levels should ideally be 30-50 ng/ml.