Why doesn't the gamma flip move intraday?

The flip is anchored to the session's settled open interest, which is published overnight. It gets set in the morning, holds for the day, and rolls the next morning.

That's intentional. A flip that recomputed against every tick would wander with noise and be useless as a reference. What moves intraday is price relative to the flip, which is exactly the read the level exists to give you.