No flaps do not need to be mass balanced. They are too rigidly attached to be able to feed energy back into the main wing structure and get a self-amplifying flutter oscillation going.
To get flutter going, the surface needs a degree of freedom of movement both up and down (like an aileron), some flexibility (springiness) in its control input connection, a center of mass that is aft of the hinge axis so that vertical motions create rotating moments about the hinge, and finally, a bit of springiness in the main structure.
A non-powered aileron (operated by cables and/or rods connected directly to the control wheel) without mass balancing tends to have this problem, so mass balancing eliminates the ability of the surface to induce flutter, in spite of its flexible interface with the main wing, by eliminating rotating moments created when the surface is vibrated vertically.
For an aileron or elevator, you don't need mass balancing if the surface is connected to the parent structure with a rigid, non-compliant attachment. You can achieve this by driving the surface hydraulically, so that the only movement of the surface that is possible is that induced by the hydraulic actuators. When you see jets that have no balance horns or offset hinge lines on ailerons or elevators, it's safe to assume it has hydraulic controls.
A flap is similar to the hydraulically operated aileron, even if its attachment is mechanical. The operating mechanism creates that same rigid connection between surface and main wing so that it can't feed back energy into the wing, and thus no balancing of the surface is required.