Unlike the Ancient Greeks (SEE), the Egyptians didn't really seem to be too keen on the idea of prophecy or fate, at least from what I know (I could be wrong). The Greeks' view on prophecy and fate was so strong and influential in their culture due to the fact that, having as a suggestive element in the Integral type, they actively searched for ways of finding information and explanations, leading them to hold reverence for oracles, and people of great wisdom or foresight. The Greeks' even sort of self-dualized their own religion by attributing humankind's transcendence to a being whose foresight is almost literally a second sight, Prometheus (ILI archetype); quite literally, they created a being that is allied with humankind's interest who has not only the Greeks' best interests at heart, but also the sight to see humankind's future (in the myth of Prometheus, you can see clearly the Greeks' distaste of through their portrayal of Prometheus's brother, Epimethius, who, in his quest of manic creativity to give creatures positive attributes, ran out of resources to give to humanity).
Enough about the Greeks, however. The Egyptians seeming distance from the prophetic tastes of the Greeks might suggest that, in fact, Ancient Egypt's integral type was a Judicious type, maybe a ego; however, it might be worthwhile to note that ego might not be as oriented to the mystical as Super Id. If you wish to find the Ancient Egyptians' integral type, a good place to start might be with their mythology; they, perhaps, might have also self-dualized themselves with their religion by projecting their suggestive element onto a being (perhaps Osiris?), or might have consequently projected their darker side or subdued sides onto an antagonizing deity (Set? -> ?). Either way, looking at their mythology should provide valuable insight.