Must a river segment be of any particular length or have certain flows in order to be eligible?

No.  The Interagency Wild & Scenic River Guidelines state, “There are no specific requirements concerning the length or the flow of an eligible river segment.  A river segment is of sufficient length if, when managed as a wild, scenic or recreational river area, the outstandingly remarkable values are protected.  Flows are sufficient if they sustain or complement the outstandingly remarkable values for which the river was designated.