I raised a question about this on this post in the comment section and was suggested by Peter Kämpf to create a new question. So here it goes: How does the extension of inboard flaps raise the effective critical angle of attack of the outer wing? And when that happens, why does the outer wing stall first without the help of slats when extension of the inboard flaps induces more lift on the whole wing, not just on the outer wing?
First it is beneficial to have an idea how the pressure field around an airfoil influences the flow around it. With powerful flaps, the suction peak on the upper side is already well developed at smaller angles of attack, so the surrounding air will be accelerated towards that low pressure area.
Now you need to extend that mental picture to 3D. The inner wing has those flaps deployed and, consequently, a suction peak near the leading edge and low pressure on the whole upper side. This will also suck in air from the side. As a consequence, the flow moving towards the outer wing will see a similar upward acceleration as does the flow streaming towards the inner wing, plus a sideways acceleration. This acceleration increases the local angle of attack at the leading edge of both wing sections. If the outer wing was already close to its stall angle of attack before the flaps were lowered, now the increased angle of attack will push the flow beyond the stall condition.
The geometrical angle of attack (measured as the angle between the flow direction at infinity and the reference length of the airfoil) did not change. The "real" angle of attack as experienced by the outer wing, however, will produce a flow similar to what would normally only be experienced at a higher geometrical angle of attack. This moves the outer wing into the stall region when the inner wing still works in the linear realm. This can lead to asymmetric stalls which produce a strong and sudden rolling moment, and at low altitude that is the last thing you need while lining up with the runway.
Adding slats will move the stall angle of attack up a few degrees, and now it will again be the inner wing which stalls first, as it should.