When we are talking flap reflex position is it relative to the wing chord or
the aircraft longitudinal axis? What is the gain from 0 degrees to the
proper reflex position?

Bill,

 

With respect to 320s and 360s, The faired in position of the flaps is -7 degrees from what would be the design normal wing chord line.  This is the cruise configuration and results in the tremendous drag reduction of the wing (if built and finished properly).  If one was to look from the wingtip to the fuselage with the flaps in the reflex position (faired in to the fuselage filet), one can see the corner (valley) formed at the intersection of the wing TE and the flap LE.

 

As the flap is moved to the 0 degree position, there is a strong nose down pitching moment and a significant increase in drag such that the same power setting results in a 10-15 Knot reduction in speed. The more the flap is extended, the more pitching moment and drag - although, after about 10 degrees down, the drag seems to increase more than the pitching moment.

 

I did some reporting about a year ago about slow flight, flap position, drag (loss of airspeed) and AOA.  I am sure a search of the archives would turn something up.