If you don’t have enough preload the wheel will clonk from side to side (eventually) as the bearings will run loose. It won’t flex.
If you have the right preload there will be no clonk.
If you have too much preload, the hub will drag.
I reckon what you’ve got going on is low spoke count, low tension or a poor wheel. Or not enough clearance. Wheels flex when you sprint, IIRC worst case for rubbing is a stiff rim and low spoke count/low tension.
How much space between tyre and chainstays in the stand? (You might just need smaller tyres, just had to deal with this for a mate, large 23s on wide rims were rubbing the stays)