This depends on how you are defining the contribution (flow) generated by each stream. Flows usually depend from multiple parameters: contributing area, precipitation, etc. If you have the equations and the underlying data to compute the flows (or some know flows) you could use the flows directly to assess the contribution. Otherwise you need to decide how to define the "contribution" you are going to use to rank the streams (e.g. contributing area).
Christine Dartiguenave
Esri Water Resources Team