Now . . . the rest of the story. I really enjoy trying to understand what was going on in the design meeting back then.
After finding a 1933 NACA paper on split flaps, it became clear why 8 degrees was selected as the "Maneuver" setting for the P-38. There is a much later paper I think in 1944 which pins down all the basic flap types we use today and it covers dive flaps as well. The war offered tremendous advances in aeronautics knowledge without question.
Some will say nay these are hybrid Fowler flaps which is right but in that the first 8 degree tilt they are split flaps since they are yet to slide back.
Split flaps( a Wright brothers invention I think) are pretty good flaps until around 12 degrees. After 12 degrees more or less, the lift addition due to the flaps goes negative but drag continues to go up. On the P38, after eight degrees deflection, the Fowler part plays in letting the flap slide back as well as turn down altering the airfoil shape greatly improving lift but at a higher cost in drag over the first 8 degrees.
At 8 degrees flap, you have the best efficiency for lift addition verses drag. Not the peak lift which happens at 50% flaps best I can tell but at 8 degrees the biggest bang for the buck you might say. After 50% flaps, some lift might be gained but the intent of the flap at this point is to increase drag dramatically.
I am pretty sure of this but I am a Mechanical Engineer, not an Aeronautical Engineer. Interesting no matter how you look at the P38.