Hi Valdis
Machines looking good.
If you have a couple of V blocks you could support the screw in the blocks and put a DTI on the diameter that inserts into the block rotate the nut and record the runout. no idea what the tolerance is for the positioning of the flats but it could be +/- 0.5mm from centre. Dean might be able to better advise, as he is working with this stuff all the time, but if you measure as directed you have better information to give to Fred.
Regards
Mike