The current firmware (2.1.6) will log flow value at the end of each program (or more precisely, when the running queue turns from non-empty to empty). It records the total amount of pulses (flow count) during the program run. Note that it does not convert this number to volume automatically, instead, you can take this count and multiply it with the flow pulse rate to convert it to actual volume (L or gallon).
The API document:
last page documents how to use the jl command to retrieve flow sensing log values. Note that you need to use the type=fl parameter as described. Without it the output will not contain flow sensor data.
There is also a real-time flow sensor variable flcrt and associated time interval flwrt. Refer to API document page 2 for descriptions. The real-time values are not logged, due to the concern that it may generate a large amount of log data (it updates every 30 seconds). But if needed it can certainly be logged.