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Spoke washers are needed when the hole is too big for the spoke. If your holes are drilled at 2.5-2.6 mm and you use a spoke with a 2 mm J bend, then a washer helps reducing movement during the load and unload cycles and fatigue. It protects both the spoke and the flange.
Old Campagnolo hubs have very tiny holes, same as most Shimano hubs modern and vintage, so washers are not needed. The thickness of the flange is irrelevant
Cheers.
Probably is narrower than that.
Had another go on the way home so swapped back to a singlespeed wheel for just now anyway.