I came across this video of the master himself demonstrating proper flute embouchure and flexibilty. There’s not much I can add.
Sir James Galway:
Try practicing his method this week with your Flute Flips and Octave Studies. Make sure to use a mirror so you can see what your embouchure looks like and if you are doing these exercises correctly.
The most common mistakes I see:
1. Rolling In/Rolling Out to make notes go higher or lower
2. Forcing high notes out with more (or faster) air
3. The dreaded “Smiley Face” embouchure
Avoid these at all costs!! Good luck!!