As CINC, President Clinton enjoys all of the benefits received by military personnel. The CINC's family, as well, enjoys the same benefits and privileges afforded to families of military personnel.
By Constitutional law, therefore, the president and his family occupy military-related status with one exception. Because the Office of The President is a Constitutional separation of power the CINC cannot be subject to any article of the Uniform Code of Military Justice. Likewise, no military family member, (whether the spouse or child of a military person, or the Commander in Chief) can be subject to the UCMJ.
With these facts in mind, because Chelsea (pronounced, Chel-see-uh) Clinton enjoys the same benefits and priveleges shared by children of military personnel, is Chelsea Clinton a "military brat"?
The United States Military Brats Photograph Museum and Registry