Just to clarify my question, I understand that the pitch down moment from flap extension is not caused from the increase in lift. I don't know if HTC models the change in location of the center of pressure from flap extension on a cambered airfoil but I assume that the pitch up in Aces High is caused by increased lift.
What I don't understand is the interaction of a pitch down moment and the increased lift when extending flaps. The P-38 POH mentions both and I don't expect it would drop it's nose and climb.
Well, this is where things start to get complicated. You are correct in identifying the discrepancy between the P-38 POH and what happens in-game. The P-47 does the same thing--there may be others that should but don't--I don't know. Not all aircraft will experience a nose-down pitching moment from flap deployment. I'll go ahead and profess I won't be able to describe the entirety of issues within a short post. The best thing I can recommend is to do some reading online. Even Wiki has some decent aerodynamics pages. Ultimately the net pitching moment of the aircraft includes a lot of variables, but read about both the center of pressure, aerodynamic center, and pitching moments. What happens in the P-38 POH is that using the flaps creates a negative (nose down) net pitching moment, whereas what happens in-game is a positive (nose up) net pitching moment.
To answer your last question though, Like Colombo said, flaps increase camber, not AoA. Generally speaking, camber increases lift at the same angle of attack, so that at an even lower angle of attack, the wing could produce the same lift, theoretically. So, you could have a lower angle of attack without sacrificing lift generation, and ultimately, this is another benefit of flaps for landing, as a steeper approach can be made (increasing the pilots view of the runway environment) without sacrificing lift generation.