In the National Hydrography Dataset there's a FlowDir field.
According to https://www.townofnewipswich.org/sites/g/files/vyhlif4766/f/uploads/dataset_dictionary.pdf the two possible values for FlowDir are 1 for "with digitized" and 0 for "uninitialized".
According to https://nhd.usgs.gov/userGuide/Robohelpfiles/NHD_User_Guide/Interactive_Tutorials/Module_2/Navigating_the_Network/Navigating_the_Network.htm "Flow direction is from the ‘Start’ junction to the ‘End’ junction. If flow direction is incorrect, NHDFlowline features may be ‘flipped’ to correct the flow direction.".
The shapefile has a sequence of coordinates. Maybe the first coordinate in this sequence is the "start"?
Exception executing: 'select * from NHDFlowlineVAA.dbf One or more errors occurred. - The provider could not determine the Decimal value. For example, the row was just created, the default for the Decimal column was not available, and the consumer had not yet set a new Decimal value.
OSGeo4W gave me 0.00000 for both of those for everything.