AEGIS is actually a legal copyright and trademark of Lockheed Martin, and SPY-6, isn't Lockheed Martin product but a competitor's, Raytheon. Just because Raytheon is another American company doesn't give it the right to use that trademark. Hence SPY-6 is never mentioned as "AEGIS" and not even by the US Navy. Why Raytheon has to give it another name, hence AMDR. For FFG(X), the requirement is to use EADS, which is really a scaled down AMDR, and called Enterprise Air Defense System, but you can't call it AEGIS because EADS is also Raytheon's not Lockheed Martin's. So no, Flight III and FFG(X) don't use AEGIS(TM) per se. Another thing is that AMDR nor EADS should not be using the AEGIS Mk. 99 fire control system, of which the mechanical SPG-62 is part of, both AMDR and EADS should be lighting up targets for missiles using digital formed beams from a second radar as both sets are dual band. In other words, these systems are not just AEGIS-like, they are more accurately should be referred to as "Post-AEGIS".
In fact, I would think that AESA based air defense systems are more "Post-Aegis", than Aegis like, including lets say the fire control system on the RN Type 45 destroyer, the FREMM ships, the frigates with the Thales APAR.