Yes, the tool is in Spatial Analyst and called Flow Length: http://resources.arcgis.com/en/help/main/10.1/index.html#//009z00000053000000
You might be able to use the Distance Accumulation tool in arcgis pro for this. Your stream network rasterization will need to be good enough so that different stream reaches use distinct sets of cells. You will also need to explicitly identify your starting locations (sources) for the measurements.
Let me know if it works.
spatial analyst team