Axle flex under load normal for freewheel hub?
As @Batman says, 2mm is VERY little clearance on a bike. It is more likely to be the frame flexing (more so the chain and seat stays) causing the tyre to move around a bit. I would see if there is a way to mount the stand a little further forward on its bracket. You want to create as much distance as you can between your stand and the tyre as possible.

Video example of a frame flexing to show what is meant by flex