Dick from the context of your comments it appears that you are using the term “angle of attack” to mean the pitch angle of the airplane with reference to the horizon. The more conventional use of the term means the angle with which the wing moves relative to the air. Using the latter definition, in a true spin the AOA is always very high and the wing is stalled. You also seem to use the term “spiral” and “spin” to mean the same thing. In a spin the wing is mostly or completely stalled, and the airspeed is relatively slow. Whereas in a spiral, the wing is not stalled and the airspeed (and “g” load) builds rapidly. To an outside observer it is sometimes hard to tell the deference.

So far no one has defined “flat” spin. An airplane has a normal spin mode that results from a yawing moment introduced at or slightly before the wing stalls. Typically full up elevator and full rudder deflection is held as the spin becomes stabilized. The resulting spin may be steep or flat and may or may not be recoverable depending on the configuration. The various factors mentioned (cg., distribution of side area, inertia, etc.) all effect the character of the normal spin mode. Use of ailerons during the spin may steepen or flatten the spin as will use of power and varying rudder and elevator deflection. When I said that a “flat” spin wasn’t a maneuver it is because the spin characteristics of an airplane are fixed by the configuration and control deflections normally have only moderate effect. An exception may be 3D type models that are designed to operate in a stalled condition using high power and thrust deflection to force the machine into maneuvers that would not be possible with aerodynamic forces alone.

As to whether a spin is “flat” or not is a fairly arbitrary definition. It obviously involves the pitch angle, but also is often used to describe a spin that is not recoverable. The flatter the pitch angle during a spin the more likely the rudder and elevator will be in the wake of the stalled wing and lose effectiveness. The slow descent mentioned in several comments, is also typical of a true flat spin. The wing is stalled and in a high drag condition and the descent resembles that of a free flight model with the dethermalizer deployed except with a rotation.

Bruce, when I commented that a flat spin requires a rear cg, I was referring to typical trainer type models. As the cg is moved rearward, the spin will flatten until at some point it will obviously qualify.

Dick, I have only flown the two control Ercoupe. I tried every way to stall it including zooms from a dive, and it really won't stall. There is just not enough elevator to stall the wing. Obviously if it can't stall, it can't spin. It will however build up a fairly rapid rate of descent in sort of a mush. It's really a strange airplane to fly.