Its not really that complex. The whole point of the VAT system is that the end user pays 17.5%, period. When you go to a UK flight school and buy services from them you are the end user and the one that benefits from these.
The only way around it is to setup a company and register for VAT but then you will fall down if HMC&E ask you what your intended business is once the training is over. That is because unless you are planning to land a job which allows you to invoice for your services and thus charge VAT to your client then you will never ever be in a position to charge VAT. They will also more than likely require some sort of evidence that you intend to carry on this company of yours as a taxable activity generating income and hence VAT which will be charged onto some punter.
You of course also get hit for the other reasons that your accountant has advised by the revenue.