A primary use of the Flow Length tool is to calculate the length of the longest flow path within a given basin. This measure is often used to calculate the time of concentration of a basin. This would be done using the UPSTREAM option.
Command line/Scripting
Flow Length can also be used to create distance-area diagrams of hypothetical rainfall and runoff events using the weight raster as an impedance to movement downslope.
Map Algebra/ArcObjects
The FlowLength command can also be used to create distance-area diagrams of hypothetical rainfall and runoff events using the {weight_grid} as an impedance to movement downslope.