The only way you can claim the vat back will be if you are working as an independent contractor (i.e: freelance self employed instructor) when you finish your course. However the money you are funding your course with is coming from someother source and is not generated by flying based revenue.
That is anything you buy for your "business" you can claim vat on, but if your current line of work is not flying then it is hard to justify an FI rating is for your business.
As a restricted flying instructor you would not comply with IR35 regulations (an unrestricted instructor can work around the regs and be complaint) therefore cannot work as a self employed instructor initially. So I would have thought no you can't claim back the vat.