As far as the type of privilege, consider the privilege of immunity from arrest and accusations of libel etc., that members of Congress enjoy - but only within the legislature. This is a quite limited one, contingent on being a lawmaker and being engaged on legislative business. I mistakenly thought that this would be obvious from a reading of the text.
Of course I am not arguing that flying is a fundamental right. I rather describe it a privilege precisely because it is not fundamental, as observed upthread: https://news.ycombinator.com/item?id=5467700