I don't know where you are, but our experience might help. DS was not allowed to skip *into* kindergarten, even though everyone knew he should, but the law did allow him to skip *over* kindergarten the next year.
This is what my DS did, too. And it worked well for him. He had done two years of preschool so adjusting to "doing school" wasn't an issue. Once the principal and teachers were able to see him and meet him and understood that he could sit still, listen, do the work, and take care of himself, they were willing to let him go straight to first.
On the other had, most educators find kindergarten to be indespensible, but since 1st grade tends to be slightly more academic, showing that your child has mastered all the 1st grade skills and has school experience might be helpful.
