Are there any restrictions on overflights above wild and scenic rivers?

No. There are no special provisions limiting overflights of components of the National Wild & Scenic Rivers System. Certain designated wild and scenic rivers are located by coincidence within restricted overflight areas, but were not the cause of the restriction. Altitude restrictions for civil aircraft in the United States under Federal Aviation Administration (FAA) regulations (e.g, 14 CFR 91.119 and 91.515 which apply to U.S. airspace) and altitude guidelines in the Airman’s Information Manual (Section 4, paragraph 7-4-6) apply to certain chartered areas. The FAA has entered into memorandums of understanding with specific federal agencies in identifying certain parks, monuments, recreation areas, riverways, refuges, wilderness, and other special areas where aircraft noise or safety is a concern. Some river-administering agencies have additional restrictions on aircraft operations, but these are promulgated under authorities other than the Wild & Scenic Rivers Act.

Source
Interagency Wild & Scenic Rivers Council