I have looked into the income tax side of this from a training company / airline point of view and a summary of my conclusions is as follows. Note that I have not looked at the VAT reclaim / self employed instructor issue but believe Whirlygig is right - although I doubt you would be able to claim the VAT back in the first place - at least until you are revenue earning and thus charging VAT on.
The way I believe a tax efficient structure would work is -
1 Student is offered a provisional position with airline
2 Student pays a bond to the airline to cover the cost of the training (no VAT)
3 Student completes training and is given position within airline.
4 Airline pays the student a (normally) reduced salary plus a monthly bond repayment
5 The bond repayment is not income (repayment of loan) and therefore not taxable as income.
Result
1 Student has not paid VAT, airline has but can reclaim in the normal way.
2 Student has had tax and NI relief on course costs.
Note that rules change and any scheme would need HMRC clearance. This is just to show you the sort of hoops you need to go through in order to have a chance of setting such a scheme up. As an individual (no airline contract) you cannot offset the costs against tax.
Looking through all this, what has "really" happened - who has paid for the course, the student or the airline? This depends on the amount of "salary deduction" imposed by the airline. If none then the airline has effectively paid for it with the student just lending (the bond) it the money. The amount the student has its salary reduced is the extent to which they are funding it.
Most schemes I have heard of involve a significantly reduced salary for a finite period. However, take home pay may be the same or higher than a "normal" salary as there is no tax on the bond repayment