how to check whether a flow network contains unique maximum flow?
Find a maximum flow.  Then create m new flow networks: one for each edge in the maximum flow.  In each new configuration, reduce the capacity of one of the edges to an amount just below its flow.  Find the maximum flow on each of the new flow networks.  If any of the new configurations generate the same maximum flow value as the original graph, then that new flow is also a maximum flow in the original graph.  Hence, the original maximum flow is not unique.