This might not work as well as you want it to... Pull too hard and it will strip the insulating coating off the surface of the mag wire, making it useless.
Two sets of rollers, in pairs that are pressed together to get a good grip. I suggest wood for some softness on the coating. Pass the wire through one pair of rollers and out with a 90 degree turn so that the wire has to be in contact with a roller for a 1/4 turn. coming out, go through a second pair of rollers much the same way. This time, the roller point in a direction 90 degrees to the first pair of rollers, so that they can roll out kinds that were not rolled out by the first pair.
What comes off of a contraption such as that will want to curl up so you might as well be winding it onto a spool as you pull the wire through. To get some tension in the rollers you'll need to have some friction on them. That's what I can come up with off the top of my head but how well it works depends entirely on little subtle decisions and choices you would make as you build this machine.