In California there is a licensing program for pyrotechnics. Pyrotechnics being defined in the California State health and safety code Title 19. The licenes are issued through the state fire marshal dept. of forrestry. One of the licenses available is a performers lcense which covers the use of black powder and other pyrotechnic devices for stage performance, re enactment, photogrphy and hobbiests. It has been a long while since I have reviewed title 9, however as I remember it, the licenese allows the bearer to take leagal responsibility for the safety of the display. It does not constitute a permit for the display. Permits are isued by the local authority having jurisdiction (AHJ).
The AHJ may be the city, the local fire department, the park service or even the county fire authority. You would need to go back to the park service and inquire as to who is the AHJ and then follow through with filling for a permit if necessary. Not all AHJ's require permits or even licensing. For others it is a touchy subject, particulaly if they have a record of accidents in the past.
As far as the BATF is concerned... Their domain is the sale, transportation and storage of pyrotechnic products. They issue individual licensing for all 3 items and do spot ispections on storage facilities to ensure that the product is being stored in a safe manner. They do NOT issue permits for displays.
Hope this helps.