Do/why don't spaceplanes suffer from flutter?
Not Shuttle specific, but there are generally two ways to prevent flutter of a control surface; for a manually operated surface, you balance it to put the surface's CG at or slightly forward of its hinge line, so that motions of the parent surface have a neutral (if CG on the hinge line) or counteracting (if CG is forward of the hinge line) influence on exciting sympathetic motion in the surface (that is, if the wing flexes up, with the CG aft the surface it &quot;trails&quot; the motion and displaces down relative to the wing attachment, putting it on the hinge line neutralizes this effect, and putting it forward of the hinge line has the opposite effect, creating an inertial moment in the same direction as the wing motion).
If the surface is hydraulically powered using irreversible hydraulic actuators, balancing of the surface generally isn't required and flutter protection is from the rigidity of the hydraulic connection (both in holding the surface from moving, and also acting as a passive damper when unpressurized). You can usually tell an airplane with irreversible hydraulics because there are no tabs or balance horns, or offset hinge lines, and the center of gravity of the surface will be some distance aft of the hinge axis.
So jets with irreversible hydraulic controls typically have unbalanced control surfaces that depend on the hydraulic actuators themselves for flutter prevention, and may also require additional passive damper units if the number of actuators used doesn't meet the minimum damping requirements following loss of an actuator. Service backlash limits for surface hinge attachments and actuator connections (resulting in surface free play) are largely a function of maintaining the rigidity of the system for flutter resistance.
The Shuttle having hydraulically driven control surfaces, you can be sure that flutter resistance is ultimately coming from the hydraulic actuators and the stiffness of the connections and structure (I don't know if the shuttle uses dedicated flutter dampers to back up the actuators).