to ozspit - lowering the flaps does not decrease the AOA, it increases it. Hence the increased lift. Since the AOA is now higher than the wingtips, the root gets to stalling AOA before the tips.

Lowering flaps will increase lift, as I said to a point. The flaps change the camber of the airfoil, and increase the AOA, and sometimes increase the wing area (fowler type). If all things remain equal, then yes, the plane will continue to climb if the AIRSPEED (not the power) remains the same. Well, since we all know that flap deployment, in addition to those other benefits, also increases drag, then it will require an increase in power to maintain the same airspeed. If you want to keep the climb with flaps, you have to increase the power to overcome the drag. So, why does the aircraft balloon when the flaps are lowered? The aircraft is trimmed for level flight at a certain stable airspeed. Change one parameter - the flaps. Now with this huge increase in lift, the aircraft thinks it is flying much faster. With the plane trimmed as when it was configured clean, it begins to climb and tries to return to balanced, trimmed flight. It slows down when the nose balloons, until the airspeed again stabilzes to the trimmed airspeed - nose lowers and eventually begins a stable descent at the trimmed airspeed. Why? Because now at that same airspeed, there is increased drag - so to maintain that airspeed (remember, we have not changed anything other than lowering the flaps), the nose has to come down, hence the plane descends, but at the original airspeed. So we can descend with flaps at the same airspeed we were maintaining level flight with a clean wing. Which is why they are beneficial at slow speeds on approach. You can maintain a safer margin above the stall by carrying more power (to maintain your airspeed) but also be descending. Balanced flight has four EQUAL parts - lift, weight (gravity), thrust and drag. Change one, and it will cause the plane to try to reach that equilibrium again all by itself.

Try it. Take your plane to a safe altitude at say 1/3 throttle. Trim for level flight hands off. Lower the flaps to say 1/2. Do not change the power setting. Watch what happens. The plane will balloon, then slow, then the nose will fall through. It will stabilize in a descent at the original airspeed you deployed the flaps.