If I’m a 1099 contractor, as a flight instructor I only get paid for the hours I fly so can my boss legally make me work the desk with no pay?

IF you are actually an independent contractor, then you are paid only as per the agreement or contract between you and your client (your "boss"). If you agreed to only be paid for flight hours, that would be legally.

The more significant question, however, is whether you actually are an independent contractor. For the full test of who is and  is not an independent contractor, go to the U.S. Department of Labor website; in brief, however, an independent contractor has at least some degree of "independence." For example, he can determine mostly, if not entirely, his own hours and location (he could be required to come in for meetings, etc.); he determines how he does his job (so no one looks over his shoulder and says "do paperwork now"); he typically has more than one client, if not simultaneously at least in succession; he is responsible for marketing his own services; etc.

If the way you work and the relationship you have with your boss does not meet the criteria to be an independent  contractor, you may in fact be an employee--what you or he want to call you doesn't matter; all that matters is the actual nature of the work.

If you are actually an employee, you MUST be paid for all hours worked, including overtime when and if applicable; you should have the employer pay the employer share of FICA and make unemployment insurance contributions; you may be entitled to benefits. If you think that it might be the case you are actually an employee mischaracterized as an independent contractor, you should either speak with an employment law attorney or contact your state department of labor.