I don't know if skipping a grade or moving schools would be good for him at this stage, since his father and I got divorced about a year and a half ago. We've worked so hard on making as many things in his life as continuous and stable as possible to help him with the huge transition. Please help!
Now as for your other concerns, I know that many gifted persons have had a successful outcome from attending a regular school program. However, your son's boredom is not suprising. Many schools today teach to the middle level of the student population. Unless your state has mandated gifted education -- and almost half do -- they do not have to provide special services for your son. If gifted education is available, I always say parents should seek it out. You and his dad should meet with the school district -- scores in hand -- and see what they can offer your son, now and in the years to come.
Check out other schools in your area as well. I realize your son has had many changes in the last two years, but if a school change is needed, it's better now than a few years down the road, when he might not be performing in school due to extreme boredom. Six-year-olds can be fairly flexible. I would also suggest you and Dad read The Survival Guide for Parents of Gifted Kids by Sally Y. Walker. It has many helpful suggestions. Good luck.