Flamed, figured wood, or quilted maple AAA top, etc, do they do anything for the sound on an electric guitar, or are they simply an expensive aesthetic feature?
They're almost purely aesthetic. By far the most important tone woods on a solid body are the back of the body and the neck (not fingerboard) wood. And there's no real sonic difference at all between different types and grades of maple. Flamed maple sounds the same as quilted maple, and the number of A's is irrelevant to sound. I'm always amazed at people who buy AAAAA-maple tops and then paint them solid colors -- what's the point?