My son is 6, in kindergarten. We've been dealing with his behavior problems since he was 3, but it seemed to improve in pre-k, then get worse in kindergarten. (My son has Asperger's and ADHD). He has a lot of impulsive behavior, and the normal rewards and consequences just didn't seem to work for him. We have decided not to put him on meds for the ADHD for now, especially since it can cause growth problems. The school has a teacher's aide with him- just to help him stay on task. We have had his eyes and hearing tested, and have seen a neurologist, counselor, and occupational therapist. The advice I have gotten is to try at least 8 weeks of seeing a counselor or psychologist before considering meds.
If you have time, try to spend part of a day at the school watching so you get a better idea of when the behavior is happening, what's triggering it, and how the teacher is reacting. Make sure the teachers know you want to be involved and are willing to work with them. Ask if they have suggestions, a library for parents, specialists, etc.
We are still trying lots of different things. The other kids were fine with getting a point at the end of the day if they behaved. For my son, they have divided the day into 8 parts and he gets a sticker for each part. So that the reward or consequence is more immediate. Also, the teachers have tried to be very creative with the rewards and consequences to motivate him better. It doesn't have to be a huge, unnattainable reward. If he gets enough points, he can play with the overhead projector or do an art project. If he hits someone, he has to call from the principals office and tell me that he's in trouble. After a week, they'll have to find a new reward because he's not interested in that one any more. They also use a picture schedule to try to keep him on task.
I started eating lunch with him at school 3 days a week to prevent one of his friends from tickling him the whole time. Also, the OT does exercises to help him be able to sit in a chair for longer without getting muscle fatigue.
We switched allergy medicine, and Rhinocort(an inhaled one) appeared to improve his behavior slightly.
At home, I do not punish my son for talking all the time(except when I'm on the phone), and I let him choose a lot of the activities HE wants to do. So he behaves OK at home. At school, he is expected to sit still and be quiet all the time except for recess.
So don't give up, go to a counselor if you need to. Hopefully it will get better as he matures.