I, in fact, encountered the same problem like yours .
I am working on sediment delivery distributed model (SEDD) which i believe , i should calculate the travel time of the eroded particles along the hydraulic path, from the considered area /cell to the nearest STREAM REACH as per the definition,.(as shown in the fig )
I used flow-length tool, however it gives a hydraulic path length down till to the outlet of the basin , Not to the Nearest stream reach .