It is possible to claim the VAT back on flight training, either as an individual or as a limited company, for all expenditure up to 6 years previous to the application.
The critical point is that you need to be able to prove that you INTEND to make sales that will be VAT rated once you are qualified - note that you do not have to prove that you definitely will, as none of us can do that, but that you INTEND to.
You therefore register for VAT as an 'intending trader', any accountant will do this for you for less than £100, it's a standard form.
The good news is that if you get VAT relief and then subsequently do not trade for VAT purposes, there is no mechanism for the VAT man to claim his money back - hence the need to prove the 'intent' to trade.