I teach Kindergarten and this is an issue I deal with frequently. I'm sure you have spent a great deal of time working with your children and spending time building their background knowledge. It can be frustrating to know that your child is waiting to learn something new. However, there are a few things to consider before moving your child ahead a grade or two.
I would begin by meeting with your child's teacher. The teacher may be aware of your child's academic skills and already have a plan in place. You may want to ask how your child follows instructions, the routines that are in place, and how your child is getting along with the other students in the class. Academics are not the only things that children need to learn and develop in kindergarten. In today's society parents are so concerned with reading and math that they over look how their child is doing socially. Getting along with others is very important in school, neighborhoods, and work places. We can rush academics, but not maturity.
Another thing to think about is what will happen when your child is faced with issues in high school and college. Do you want all of the other students driving and your child is left out because he is to young. There are other areas where his age will come into play. Will he be the smallest kid in class? Maybe not a big deal in 1st grade, but it will be in high school sports.
Some children say they are bored because they would like to be playing more or are having trouble following the rules. This is understandable, but your child would suffer in 1st or 2nd grade if he is wanting to play more and /or can't follow instructions. He may not be used to the structure and expectations of a school setting. Unfortunately sitting for 5 to 10 min. and listening at the beginning of the kindergarten year is a typical and realistic expectation, some children struggle to adjust.
Your child may also be presenting as gifted now because of the time and energy you have put into his academic work. But when the other children catch up, or he is surrounded by other children who know more, how will he do? I have seen several children start out very strong, and then level off because the maturity and skills are not there yet. A 5 year old brain is very different than that of a 7 or 8 year old.
Is your child the only advanced student in the class or grade level? The teacher should be able to differentiate for the needs of the higher learners in the classroom. It may take a few weeks to get to that point, but it will be worth the wait.
I would speak to the teacher, honestly evaluate your child's maturity level and ability to interact with others, and go from there. If your child's teacher is unreceptive, ask for a meeting with the principal and teacher. Ask how the district assesses placement, and if your child should be tested.
Reading, writing, and math are all a part of a kindergarten curriculum and your child's needs should be met. But don't forget, academics are not the only important thing in kindergarten. Good Luck!!