Academies are funded through the Education Funding Agency, not through the local authority. Academies get the same level of funding for each pupil as local authority schools in the same area; their notional SEN budget is worked out in the same way; they can get top-up funding from the local authority in the same way.

Academies do get extra funding, but this is not specifically  related to SEN: it is for services that Academies have to buy for themselves. These are services that are provided by the local authority for local authority schools i.e. Speech and Language Therapy