yes assuming the stab and wing are into the airflow at the same angle when the flaps are not deployed,
and the deployment of the flaps pitches the plane (up or down) in level flight then the stab in most planes being fixed would then not be inline with the airflow (skid)
Not a skid, a skid is when the airplane is in uncoordinated flight in a turn but your point is getting there.
First, the wing always produces a nose-down pitching moment whenever it produces lift because the center of lift is behind the Center of Gravity. Remember that an airplane wants to rotate around its CG. This is nose-down moment balanced by the horizontal stab which provides a nose-up pitching moment, basically, it pushes down to counteract the upward push of the wing (how's that for a non aero description?). In stable flight, these two forces are balanced.
So, now lets say you're stabilized (not accelerating or decelerating, not climbing or descending) and trimmed for level flight with flaps up. You then drop your flaps. All flaps will always produce additional nose-down pitching moment. It's the way they work. I can actually expand that statement. All lift from the wing creates a nose-down moment regardless of whether is caused by camber or AOA because the center of lift is behind the CG. The airplane rotates around the CG and the additional lift behind the CG will want to pitch the nose down. OK, so much for the wing and flaps but what about the rest of the plane, i.e., the tail surfaces? Remember that the horizontal stab was providing a nose-up pitching moment which balanced the moment caused by the lift from the wing with flaps up but now the wing lift has increased so the nose wants to pitch down more. But what happens to the horizontal stab as the nose pitches down? It pitches up which increases the horizontal stab's AOA and increases it's lift (remember its lift acts
downward) and nose up pitching moment. In other words, you can think of it as automatically trying to oppose the increased pitching moment from the wing. So, you have a
nose-up pitching moment which is opposite of the
nose-down moment created by the flaps. You can see that whether the plane pitches up or down is a direct result of these two relationships. If the moment from the flaps is greater than the moment from the tail then the nose will pitch down. If this is reversed, and the tail has a greater moment the airplane will pitch up.
Now, this is greatly simplified as there are several other things going on though including the effect of downwash on the tail surface. Also, this is much clearer with a diagram but I still can't upload it. I hope the verbal description hasn't confused anyone.
Mace