What are the aerodynamic differences between the different types of slotted flaps?
The high energy air that passes through the slots prevents boundary layer separation over the top surface of the flap. Though, this increases drag but it improves the stall characteristics of the airfoil. In other words, we can have higher maximum lift coefficient (Cl_max) by having higher maximum angle of attack (alpha_max). So, higher the number of slots higher Cl_max one could reach, there should be a limit. In case of a fixed weight of an aircraft,a higher lift coefficient implies that one can fly at lower speed before it stalls. A comparison between different types of flaps (up to double slotted)can be found in the book Aircraft Design and Performance by Anderson. 

Source:
The same book.