On White's HP i can see two arrangements, one with a big V- flap ( split flap) and one with a small V-flap (flipping split flap)
I think that one with the biggger flap has been the first one.
This setup has to be trimmed much more, 'cause you have three interacting components.
For easyness only upwind
-softsail whose camber is controlled via track at the end of the boom
--MastFoil whose amount of lift is controlled via it's positive angle to the apparent wind
--flap, whose angle to the centerline of the Mastfoil defines again the amount of lift of the MastFoil
A complex system, a lot of telltales are needed.
This setup has a lot of variabilities, the margin of a mistake is big.
With other words , for the average sailer the setup is much too complicated.
That the big flap has been controllable over a wider range ( from 0 to about 40 degrees) shows the control arrangement in vid 40. (Note that the mizzen in the vid features the second, the smaller flap )
https://chriswhitedesigns.smugmug.com/ATLANTIC-CATAMARANS/Atlantic-47/Atlantic-47/i-RnZMM5k
https://chriswhitedesigns.smugmug.com/ATLANTIC-CATAMARANS/Atlantic-47/Atlantic-47/i-V3CHvnK
Smaller flap , also upwind.
--the MastFoil is underrotated a little --about 10 degrees positive to the apparent wind. this angle of attack is more or less universal and easy to obtain.
At this angle the Foil itself ( alone) generates lift with little drag. It is far away from flow separation and very far away from stall.
--at this angle the little flap can be set full . No separation, no stall , but much more lift for the Mastfil with only very little additional drag.
This setup is much easier!
One tacks, one flipps the flap, one rotates the foil about 10degrees to the apparent wind.
Any Sailer can do this.
A keen sailer has the option to fine-tune the Mastfoil on the new leg.
pic showing flip-flap control-unit, note the two holes.
https://chriswhitedesigns.smugmug.com/ATLANTIC-CATAMARANS/Atlantic-47/Atlantic-47/i-T9hbGr2
Tacking, note that the 10degrees are given very late after the third tack , at about 2:10
https://chriswhitedesigns.smugmug.com/ATLANTIC-CATAMARANS/Atlantic-47/Atlantic-47/i-RnZMM5k
One might ask why a flap, why not rotating the foil only for more lift ?
A higher angle of attack means earlier flow separation and much more drag.
using a flap means lower angle of attack of the foil , only little additional drag and much more lift.
About the kinematics , the mechanism of the flip-foil i don't know anything, sorry.
At least one can see lever arms connected to the bigger , tuneable flaps
http://chriswhitedesigns.com/atlantic_cats/mastfoil/update_01-12.shtml
For other solutions please search in Google Pix under " aileron mechanism" .
pogo