The basis for this problem is the age-old distinction between on the one hand a contract for services, where services are given on a self-employed basis, and on the other a contract of service, which is employment by another.
There is a lot of stuff about this on the 'Directgov' website, much of it confusing and/or ambiguous, IMHO.
However, I think it is pretty well established now that if you only give your services to one 'employer' you will struggle to convince HMRC that you are self-employed. If that principle has not been applied to instructors before now then it surely will be in the future, because other industries have been stuck with it for some time.
However, if you work for more than one flying school on days and times which you choose, provide your own clobber, essentially manage your own schedule, pay for your own renewals and medicals and are paid your pobblebeads without deduction of tax or NI, then I can't see how HMRC could argue that you were anything other than self-employed.
And yes, it beats me why HMRC should want to have a go at flying instructors anyway. Perhaps they think instructors are a highly paid species? If so then after a couple of investigations perhaps they will get the message and forget about it.