Do leading edge flaps increase the critical angle of attack?
Yes leading edge devices indeed postpone stall to a higher Angle of Attack. They are particularly useful for: 


Airfoils which are prone to leading edge stall. Deflection of the trailing edge flap creates upwash at the wing nose, which reduces stall AoA mainly on thinner wing profiles.
Aeroplanes which use lift dumpers as speed brakes. Deflection of the spoiler reduces the stall AoA, a leading edge device provides extra AoA margin.




Image source and source of info below

The four main types of leading edge devices are:



  LEADING-EDGE SLATS are small, highly cambered airfoils forward of the wing leading edge, which experience large suction forces per unit of area and reduce
  the suction forces on the basic airfoil.


Note that before deflection, the slat was part of the wing nose. Its area is mainly deflected to a new position, not extended as in the case of a trailing edge flap. 

Slat deflection does indeed change the camber, by reducing the local AoA. This potential reduction in local lift coefficient is compensated for by the changed suction forces around the nose, with a net effect of around zero. 

  KRUEGER FLAPS perform in the same way as slats, but they are thinner and more suitable for installation on thin wings. Krueger flaps are often used on the inboard part of wings, in combination with outboard slats, to obtain positive longitudinal stability in the stall.


  (PLAIN) LEADING-EDGE FLAPS (hinged noses) are less effective than slats. They are mechanically simple and rigid and partic- ularly suitable for thin airfoil sections.


  FIXED SLOTS are the simplest devices for postponing leading edge stall, but their profile drag penalty is generally prohibitive for effective cruising, except on some low-speed STOL aircraft.



The picture below plots what happens upon deflection of flaps (left) and slats (right). Flaps increase lift for a given AoA, but reduce critical AoA. Deflection of leading edge devices does not result in increase of lift at an AoA, but postpone the critical AoA - in order to obtain more lift, the AoA needs to be increased.