The only mention of the Econet Flat Box I can find is on page 76 of the Econet Design and Installation. "Flat" apparently means "F"irst "L"ine of "AT"tack and the box is an Econet testing and troubleshooting aid. It is mentioned as an alternative to Acorn's Econet Test Box but no further information is given.
The Cable Test sockets are used, not surprisingly, for testing an Econet lead. Plug one end into Cable Test (1) and the other into Cable Test (2) and then turn the knob and the green light will come on whenever the cable is correctly wired up and working.
A further use of this which I have discovered is to test the wiring on a network. If you plug an Econet lead into Cable Test (1) and then into a socket box on the network and do the same with a second Econet lead and Cable Test (2), the Flat Box will test the network cable between those two points on the network and can therefore identify incorrect wiring or cable faults.
The Signal Test socket will test what signals are being transmitted on the network. Plug an Econet lead into here and the other end into your network and the C- and C+ will light up if a clock signal is detected. The D- and D+ lamps will flash if the Box detects data being transmitted on the network.
I am not sure how the Resistance Test one works but this may relate to the additional sockets on the top of the box.