I think it depends on your district. It can be difficult. It can't hurt to place a call to this desired school, but they may bounce you back to the official route. In D2, officially, you need to fill out a transfer request form from the district HQ. It seems like they will only consider "bullying and safety" issues (I tried to transfer my older child from private to public in middle school a few years back) and they don't make it easy. Unofficially, I know families that have "jumped" early in the year to a new (and by new, I mean newly opened) school that might have openings, by calling the parent coordinator and making inquiries. A very popular school will not have openings. Many schools "lose" a few students in 7th to Hunter (especially those aforementioned popular schools) and you may get an indication as early as March when those acceptances are announced.
Be wary, however, of jumping from the frying pan to the fire. Middle school can be a difficult transition academically as it's a time when organization and executive functioning abilities are pressured for the first time. This is often an age when learning disabilities in high-functioning kids are first diagnosed. Be certain that there's not an underlying issue that needs to be addressed. If the administration is helpful at his present school, see if you can't get him tested. There's often a waiting list, so many parents bite the bullet and pay out of pocket.
