Trick argument back at you............
How can maximum lift be increased ???
If it can be increased - it was never at max.
Ask NACA..... chuckle......
Actually, the plots show the max CL from the airfoil and the max CL obtained when plain flaps are deployed. Most that I've seen were just that, plain flaps. simple flaps. whatever the name...... But the application is very much like we'd see with a lot of models whether or not the flap is a plate that is flat against the bottom of the airfoil or is the rear of the airfoil. But that said, I've seen a couple where the CL was reported for the "rear of the airfoil" deflected and not deflected. And the plots weren't only the old NACA ones.
If you'd like to twist the definition of flaps, kewl. I'll go along with that. But really, most everyone is discussing having them things that stick down versus not having them things that stick down sticking down.
And a couple of the plots I've seen show something like a ClarkY giving around 1.? CL for max CL of the airfoil, but having a dotted line showing a simple flap hinged somewhere around .8C. And the CL for that airfoil with that flap deflected had it's own traces on the plot and the traces went WAY WAY up the chart above the "non flapped" line.
I'm on your side all the way about slats and flaps that extend, but gotta argue (with tricks or not) that almost every book I've read states that flaps increase the CL you'd expect from a specific airfoil by a very significant amount over what you'd get with that airfoil without flaps.