Hi S.,
Could you check with the school about skipping a grade? Schools try to fit all kids of a certain age into a certain mold, and it doesn't work sometimes. If he's failing they may not at first understand that he seems to be advanced, so they may need to test him, which hopefully he'll do well on (if it's challenging to him).
Since he's in 6th grade he'll likely be in middle school next year, but I imagine he could be tested now to go directly to 8th grade. The school admin may also be able to let him do some 7th grade classes & some 8th grade. I skipped 1st grade, and this is how they transitioned me.
OTOH, the social connections your son has with his current group of friends can suffer. That was the downfall for me.
If this doesn't work, what about homeschooling him? By 6th/7th grade he may be able/willing to do some school himself and then have neighborhood friends, hs social groups. Homeschool is mainstream nowadays, and socialization while hsing is relatively easy. Also you as the parent do not need to be the only teacher. Your grandmother might be willing to help, and/or you may have options for part-time group activities at private or public school.
Hope this helps! Best of luck. This is potentially a "good" problem to have. :)