gesres

This definition is not used anywhere in the aerodynamic literature and I don't find it referenced in the icing document. I mentioned previously the concept of "absolute angle of attack", but that's based on the zero lift line, not this imaginary line you draw from the trailing edge of the deflected flap to the leading edge. The absolute AoA is normally used in stability and control mathematics, but only due to how it simplifies the calculations.

Some books may refer to the line you define as "effective" AoA, but that is a pedagogical strategy to describe how flaps work. Your own Shevell book does this, but then turns around to say that flaps increase the lift coefficient without changing the AoA, which is a reversion to the standard terminology. If you have "Theory of Wing Sections" you'll see that NACA uses the definition of the AoA that I have provided, even since the early 1930's. All of their airfoil data presupposes this definition and the data is meaningless with any other.

When contemplating any scientific theory, you need to start with the definitions they give you and reason forward from those; you can't start with your presuppositions and work backward to the definitions. I have learned this the hard way.