the wing camber and AOA both increase
Let's look at the lift equation:
$Lift$ = Air density x wing area x Lift Coefficient x V$^2$
Lift Coefficient factor can be expressed as airfoil type (camber) at a given AOA.
When you lower flaps (for that portion of the wing) camber and AOA are indeed both increased but... the wing is producing more lift at that speed, which would encourage the pilot to lower AOA for the entire plane. This is a good move to prevent tip stalls, but ...
Lowering flaps also increases drag, so more throttle is generally required to maintain airspeed.
Slats lower AOA when deployed but increase camber. We can see that putting flaps near the fuselage and slats near the wing tips is a great safety combination.
Earlier aircraft (and many models) use "wing washout" for the same effect. The benefits of retractable slats and flaps are that: at higher cruise speeds "pulling them in" yields an improvement in fuel consumption efficiency from less drag.
increase AOA and critical AOA?
Better said that flaps will lower your stall speed (which you do not want to be near at low altitude) due to increase in camber. For example, when aborting an approach to landing with flaps, avoid the temptation to yank the nose skyward to climb out. Add power. At higher flaps settings, your stall angle relative to the horizon may be lower than with flaps up.
Significant increases in critical AOA can be had with leading edge slots, but again with significant drag penalty, requiring more power.