From what you've written, your child has essentially been a shut-in. You need to give him the ability to socialize, not so much time with flash cards. I see this as an emergency situation. No child should get to age 5 spending all his time with a parent or caretaker. Academics will come-- address his social needs and overall happiness first.
This... especially since not only was all his time with a parent or caretaker, but too little of that time was interactive. Children can still learn valuable social skills without play dates if they're frequently interacting with multiple adults who actively engage with them at the proper level, model successful behaviors, etc. Children who play by themselves all day learn nothing to help them socially.
The school has obviously picked up on the fact that he's completely unprepared to deal with K on a social level, and disqualified him for early entry based on that lack of "maturity." Another year won't make any difference if he's not practicing the requisite skills during that year.
