Some airplanes flat spin inverted better because there is more air flow over the fin and rudder or less disturbed air. Think about it... when in an upright spin the air flow to the upright fin is blocked by the shadow of the wing as it is pancaking in. That is why some planes need a burst of power or put into a dive to get them out of a flat spin. Same goes for Harriers... some say thier plane will not wing rock in inverted Harriers because there is little disturbed air to the rudder inverted. I have a little .15 plane I designed that would flat spin like a frisby but it took nearly full power to get it back or a quick hit of power and down elevator when it was in an upright spin. Inverted it did not have this tendancy... probably needs more rudder area. I had an RC Nobler back in the 70's that did the prettiest flat spins because of the short coupling but it didnt have enough rudder area to recover easily and I pancaked that plane in three times and did very little damage cause it went in so slow.
Once I get into a regular spin I add power and start feeding in opposite aileron till it gets flat enough.

Smooth Flying...

Wayne G.