This is the famous Handley Page eight element airfoil modified from an RAF 19 section. It develops its maximum lift at 42° and was published first on February 17, 1921, in a lecture given by Frederick Handley Page to the Royal Aeronautical Society and in The Aeronautical Journal in June 1921, page 263.
A single-element airfoil would stall much earlier. Here, every element but the first sits in the downwash of the preceding element. Please note the strong negative incidence of the first element: This allows it to still experience attached flow, despite an overall angle of attack of 42°. Also, the angle is measured using the connection between the leading edge of the first and the trailing edge of the last airfoil, and their staggering makes the reference line so steep. As drawn, flow is coming horizontally from the left.
The hand-drawn lines are only remotely indicative of the streamlines around this airfoil. A plot of the pressure distribution was published by Valeriu Dragan:
The design and function of multi-element airfoils is best described by the classic 1975 article by A.M.O. Smith, “High-Lift Aerodynamics”, 37th Wright Brothers Lecture, Journal of Aircraft, Vol. 12, No. 6, June 1975.
That the bit of air which passes through the small gaps is able to keep the flow attached is due to the new boundary layer which is formed on each airfoil. Whereas the boundary layer of a single element airfoil will be worn down by wall friction, here a new and fresh boundary layer is able to raise the pressure on the upper side just a bit before the next one takes over. Once the flow at the surface is attached to the airfoil, suction forces will make sure that the outer flow also follows the contour. Flow separation happens either directly at the surface or not at all.
Smith shows in his article that every new element will be able to raise the lift coefficient a bit more, and in total a much stronger pressure rise is possible, consequently allowing a much lower pressure over the upper side of the first elements, and thus a higher lift coefficient for the full assembly.
However, a new boundary layer means high friction drag due to the high shear gradient of a fresh and thin boundary layer. Therefore, the drag increase contributed by an additional element is higher than the lift increase, so this can only be used when drag is secondary and maximum lift is very important: During approach and landing.