Axle flex under load normal for freewheel hub? When using a freewheel'd hub is it normal for the drive side of the axle to flex a little bit?  

I replaced the kickstand on my bike and the new one sits closer to the rear tire with about 2 mm clearance.  However, since I did this I picked up a squeak/rub, but only when I'm applying power.  I back off the power or coast and the squeak goes away.  Upon closer inspection I have found that the tire is rubbing in spots, but with very little force.  

This is the same setup in another question of mine where I was having axle troubles (Reoccurring Bent Axles, any reasons or upgrades?).  I have replaced said axle with a stronger one (so the LBS told me) close to the same time, and so far, no other major issues.  The wheel is true, but tire does have a spot or 2 where it is out of line.  I have checked for play in the bearings, but none is there.

Given that it only rubs though when applying power and it doesn't at all when on the stand then I'm lead to believe that the driving forces is causing the drive side of the wheel to move forward and causing my issue.  Am I right here and is it normal?  If it is normal, is such a flex going to be a bent axle later?
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