Client.flush() is empty as defined in Print.h. It might be defined in the specific network client implementation but you didn't tell us what you're using.
Usually you would wait for a server response before closing the channel, but that depends on the protocol used (which you also didn't tell us).
BTW, the Ethernet library sends every byte immediately so a flush is not needed usually. Are you sure your server is not expecting the client to wait for an answer?