As a very generic statement it can be said, that flaps are the item on most aircraft which are routinely operated closest to thier strength limit. Aircraft are very often flown only a few kts away from the maximum speed for the selected flap setting, while the overall wing is rarely flown close to its limits, neither in g´s nor in speed.
Additionally flaps are subjected to high relative motion due to wing bending and to high vibration from the engine jetblast, reverser turbulence or spoiler turbulence.
No designer dares to design flaps just strong enough to meet the requirements, typically you have to add quite an additional strength margin to keep the operators (reasonably) happy.
There are several NACA reports with detailed pressure distribution or flap loading measurement available on the web.