Hi Nathan,
If you are going to flip your painting, then you also need to flip your source photo or if you are working from life, use two mirrors for the reference image and compare those images, rather that original and flipped.
Comparing an original and a flipped will get you into all sorts of messes because faces are asymmetrical.
If you were to cut the painting in half and copy one half and flip it and join the two together, you will get another completely different person.
This aspect of faces becomes more obvious the older the person is.
I have seen this done with a photo of a famous Italian opera singer and you get two completely different people, one fat and one thin, who kind of look like the original but something is not right.
This is why we hate photos of ourselves and probably why, when we show our masterpiece to the subject, they stand and ponder and don't say anything for a long time..