Does anybody here have any suggestions on how you would "fly" an AoA indicator in normal operations? And how you would include it in your scan?
Well, how did they use it in the Concorde? Why was it there?
In carrier operations, it is the primary speed indicator for approach to landing. At approach speeds, it is operating in its most accurate range and precise speed control is essential to a good carrier landing. Every aircraft that I flew, the AoA indicator was calibrated to be "on speed" at 1.3 Vstall in the approach configuration. No matter what your weight, you were at 1.3 Vstall when the AoA indicated "on speed".
AoA is not useful at cruise speeds because the variation of AoA with speed is much smaller than at approach speeds. However, it could have been useful to the crew of AF447 in understanding their situation had they been trained to understand it.
As far as incorporating it into the scan, it is just like any other instrument. In fact, it is an excellent cross check against the airspeed indicator.