The main wing element of these airfoils was designed to a similar aerodynamic philosophy as the wingmast sections - providing for a smooth forward movement of the transition point as angle of attack increases, so as to have robust characteristics at low Reynolds numbers. The NACA 0012 provides a good section for the flap because of its front loading, which allows the whole flap to be used for the airfoil's pressure recovery. Any tendency of the flap to form a leading edge pressure peak can be suppressed by adjusting the slot gap. External flaps are separate airfoils that are positioned near the trailing edge of the main wing. They are were used on the Junkers trimotor and several ultralight aircraft.
External flaps can provide high lift with low drag and give the designer lots of flexibility.
The C506F is my own design, made for a designer working on an all-metal ultralight. The the key requirements were very high lift, ease of manufacture, and good handling qualities. Incorporated A hydrofoil design handbook prepared by Hydronautics Inc. for US Navy in mid 1960's. 313 pages total. This is the most comprehensive reference on hydrofoil design I've found.