There's generally a small amount of back and forth play in the countershaft (sprocket shaft), but not in the mainshaft. The outer basket will have a small amount of freeplay too as it spins on a pair of bearings and is not solidly mounted to the mainshaft so needs clearance. The inner hub should not have any play as it's tightened down against the collar that the outer hub spins on.

If you mean there's rotational play then this is normal, but probably not 3mm. Have to check on that. I trust that the primary drive and driven gears are off the same model ie: 21 or 28.