The index card system is basically a good idea in order to promote collaboration between home and school and to support proper classroom behavior. But there should be more than a single rating. Instead, the day should be divided into time blocks, with the potential to earn a sticker (and corresponding reward) during each time period.
Time out within the classroom (instead of trips to the office) might be a more effective strategy within the school.
It's possible that your son doesn't yet possess the impulse control to function successfully within the classroom, but I wouldn't conclude this yet.
His behavior is typical of children who display the hyperactive and impulsive sub-type of Attention-Deficit/Hyperactivity Disorder. It might be wise to consider this possibility before concluding that he's not yet prepared to function in kindergarted.
My son experienced similiar problems with his first year of Kindergarten. Inmaturity was the problem for him. We sent him when he was 5 (turned five in July). He was very ready academically but not ready as far as maturity. He was antsy in class, distracted, upset. We sent him again this year and it is like a whole new kid. He has matured so much and behaves much better in the classroom. This may not be the case with your child but I thought I would throw in my experience anyway.
Homeschooling would be an answer if you can. Public school stifles creativity in small children, especially active ones that need to be moving outside. There are many homeschoolers now. The Moore's book "Better late than Early" is excellent.