Everything constructed to resist any kind of load will "flex" under that load.
Some materials more than others.
I watch the wings of airliners flex outside my window when I fly. They can go up and down a couple of feet. Doesn't bother me. It's built into the design.
The Space Shuttle wings flex like any other aircraft's. The pressure vessel in the nose that protects the crew expands and contracts when there's pressure across the walls.
The Shuttle's external propellant tank expands and shrinks as fuel is loaded and drained. Bellows on propellant feed lines accommodate the movement.
Look at the ignition sequence in the "Riding the Boosters" video below. Look at how the entire structure moves under the loads.