I've been doing flexi schooling for my DS for 3 years, though it has been a fight with the lea (who believe, erroneously, that there is some kind of legal requirement for kids to be in full time education by age 7). We do ABA at home in mornings, and pm's at school with ABA-trained LSA. It works really well, as long as both sides give respect to each other (sometimes the ABAers have tried to ride roughshod over school's opinions, or vice versa; I've tended to be the mediator). As of last year, there is useful case law (TM versus Hounslow) which changes the presumption that school should be the first choice for education. School now has to be assessed against other forms of education (eg home ABA) acc to the child's needs. It is still the case that the Head needs to agree flexischooling, and many heads are gutless creatures who simply do the LEA's bidding (not entirely surprising, as the lea pays their salary, promotes them, fires them etc!)
I think the truth is that , often, schools are not going to be willing or able to put in the huge, patient efforts that it can take to get an ASD child reading/writing etc. That can often best be done in the quiet and calm of home. Yet full time education at home makes the social side much more tricky, and that's so crucial for some ASD kids. To me, flexischooling makes perfect sense, and I hope this govt might one day strengthen parental rights in this area.
It need not cost the LEA any more either - as they simply pro rata the normal LSA salary between home and school.
Good luck - stick to your guns, but build a good case first - could be something like, the need for one-to-one work on academics at home, and social and group work at school. Don't say it's cos he's unhappy, or they'll just try and put some piss-poor recovery plan in place. It's much harder for them to argue if you start with the child's individual needs, as they legally must loo,k at individual needs of SN kids.Good luck!