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.

Interagency Wild & Scenic Rivers Council