If the Hinton video referenced is the POF flight with the P-40, you can clearly see the 8 degree maneuver selection, and the flap panel is about halfway past the trailing edge and then Hinton demonstrates why the new flap selector with a positive detent for maneuver flaps was so necessary.
The flaps go back up a bit as he fiddles with the selector before getting all the flaps out.
You can see from the shadow in the gap between the trailing edge and flap panel that the angle is minor in the first flap position.
If you compare the deflection angle of full flaps to the first angle, visually the angle difference between the two in the video appears to be full flaps is about five times the deflection of the maneuver setting at 4:25 in the video.
It is certainly much more than twice the maneuver setting, so the visual evidence alone tells you maneuver flap definately is NOT half deflection ( 20 degrees). It is something less than 20 and there is evidence for 8 degrees being the actual deflection number.