A flap extension with zero flap angle will increase the lift L, not necessarily the lift co-efficient CL. When the extended flap are turned down with a certain angle, only then will the circulation increase, as Dook says. This will lead to a higher CL max.
I am not sure whether extension of slats have no effect on CL max, I would think that with an increase in AOA the circulation will increase at higher AOA, and therefor resulting in a higher CL max.