I don't see how today's definition of a Flip is pretty clear... if we combine them with the GOE bullets. These are two separate things unfortunately:
1. Flip takes off an inside edge - in order to emphasise the edge, skaters might try to go deep into the inside edge.
2. Very good height and distance/Good body position from take off to landing - the mechanics of the Flip are such that when you keep the edge as
shallow as possible, you maximize the force you get out of the toe tap, and transfer momentum into the air most efficiently (bigger Flip jump). Moreover, the shallow edge keeps you on as straight an entry as possible, which allows a much more controlled axis in the air, whereas the deep inside edge entry is usually more curved, leading to a loss of control in the air in comparison.
IF the point is to get GOE bullets, then the Flip should indeed be taught off a shallow edge... but seemingly the Flip jumps that tend to go off shallow insides get called (!) wrongly sometimes, which leads to lower GOE even with better aesthetics. The judges instead go with jumps with deeper inside edges, since they don't get any calls, even if they have worse aesthetics. This indeed turns into a problem - we have now defined the Flip jump based only off a deep inside edge, even though the better Flip jumps are off shallow inside edges!
It's not difficult for me to see personally that pre-CoP the definition of a Flip allowed flat/shallow outside edges. Since the difference between shallow outside/flat/shallow inside is very little, and again the momentum/quality produced is greater.
ETA: And yes... Obvious Lip is Ando's:
https://youtu.be/ibtOU8mAHCo?t=103 Fernandez changes to an outside as he's already vaulting. Ando's edge deepens along the entry curve, before she even taps.