River forecasts (flood forecasts) are made by the National Weather Service River Forecast Centers and released through local Weather Service Offices. This NOAA website has a map showing the location of the forecast centers, their areas of responsibility, and by clicking into a region the location of the gages they use. The also provide a section for long-range river flood risk.
The vast majority of current streamflow data used for these forecasts is obtained from U.S. Geological Survey streamgaging stations, but the USGS has no other responsibility or authority for making forecasts.
Learn more: Where can I find flood maps?