I find it helpful to set the mill so that it will leave the flats a little too high, and to start, mill two, opposite each other. Check the AF dimension with caliper or mike, and then adjust the setting by just enough to give the finished size you need. Then go round all six at that setting and your nuts will fit the spanner as you hoped.
PS just to avoid misunderstanding, AF means Across Flats. This method works perfectly with nuts in other systems as well as the 'Unified' or US sizes marked as AF spanners.
PPS it should also be possible to mill flats of several times the nut thickness at one go, and then part off to give the finished nuts, remembering to cut a V-groove before each parting so the nuts have a chamfer. Don't over-do the length, though, as you cannot use a steady at the free end to support the work.
Cheers, Tim