Why does stall speed decrease when flaps are deployed?
Your stall speed decreases because the $C_{L_{MAX}}$ of the wing increases with flaps deflected.

Deploying flaps increases wing camber and increases both $C_L$ and $C_D$ at the same AoA and airspeed. Depending on the type of flap, the critical AoA actually reduces: the airfoil with simple flaps deflected stalls at a lower AoA than without flaps.

 

Slats or leading edge flaps do not change the $C_L$ at the same AoA, but allow for a higher AoA and therefore higher $C_L$ before the airfoil stalls.