Within a given state (and its overall policy regarding low SES access to its state universities, including admissions and in-state financial aid related policies), higher SES students have significant advantages in opportunities during K-12 to earn the usual measures of merit for college admissions (GPA, test scores, etc.). In addition, they are less likely to be financially constrained to living with parents and commuting to a local university because that costs less than living at the university (unless the flagship offers financial aid to cover that cost). So it is no surprise that higher SES students are better represented as residential students at state flagships than they are at the same state’s other state universities.
In addition, some state flagships attract a substantial number of out-of-state students who typically come from higher SES families who can afford the higher out-of-state price and lack of out-of-state financial aid. Budget-limited state flagships see such students as bringing in much-wanted cash.