I would say start discussions as soon as possible. Full-grade accelerations seems to take a very long time in many districts. As for the how, I would set up an initial meeting with the principal and possibly the GT coordinator. They will likely want to get the curriculum director involved to talk about gaps and such.
My son skipped 1st after we were told by the school that they planned for him to go to 1st, but with subject acceleration to 3rd for reading and math. We were able to convince them to do the skip after going through the Iowa Acceleration Scales, along with noting that it would be much easier for the teacher in 2nd to differentiate one year versus the 1st grade teacher to differentiate two. In addition, all the other subjects will be grade-based, and 2nd will be closer to what your kiddo needs. Even though one skip wasn't enough for our DS, it was so much better for our kiddo in 2nd than it would have been in 1st. The struggle was that his writing skills were much poorer than his classmates, and this sounds like it's not a problem for your kiddo.
We did end up moving to an accelerated school midway through 2nd, so effectively our DS skipped 2 grades and now he has a good fit. You may want to consider asking for the double-skip, since he'll know many of the kids anyway. Something to think about anyway. Just giving our experience....
