Here's what you do. You let the teacher handle it. She needs you to allow HER to be his authority figure at school. SHE needs to give him instant consequences. It does little good, if any at all, to give more consequences at home.
He needs her to catch him, dole out whatever her consequences are, then move on. She does not need to keep telling you that he's doing this. SHE needs to handle it.
The sooner she learns this step the better off she'll be as a teacher. If she can't handle her classroom then she will have to go to her supervisors or other teachers to learn better skills.
Your son is young. Starting early isn't all that great for kids. Even if he was a genius he's socially still a much younger kid. If he's a young 7 then he'd still be in first grade, if he's almost 8 then he'd normally be in second grade. So he could be up to 2 years behind his classroom peers just because he started school early.
6-7 First Grade
7-8 Second Grade
8-9 Third Grade
9-10 Fourth Grade, etc....
My point is that he's going to have some struggles. He doesn't need to be held back or anything like that, that isn't what I'm saying. What I'm saying is that knowing he's younger and will have social problems, like talking too much, are going to be NORMAL things for his age. He shouldn't even get in much trouble for this.
We develop along a pretty consistent line. He's 7 and 7 year old kids talk in situations that we don't always want them to talk. He's normal.
His teacher needs to address this in an appropriate manner and remind him that talking is not allowed during this or that time. They need to redirect him or channel him, perhaps the teacher can have him read a passage from their text or something. Keeping his talking directed in an appropriate way.
All in all, this is a school issue and one that you should redirect back to the teacher. When kiddo comes home with a note or something saying he's been talking in class you say "It must be hard to remember this. You need to work on this in the classroom, there are times in class when you need to use your ears and not your mouth". No punishment, no lectures, nothing. The teacher needs to manage consequences AT school. This has nothing to do with "home".
If she's really not capable to figure this out perhaps you can ask the district counselor to come in and observe her class so they can give her ideas on how to manage this. Ulterior motive would be that the counselor is observing the teacher and would be able to offer them some needed ideas in how to manage a classroom better.