I imagine that these types of legacies, direct descendants of the founder, hoping to attend the law school that their ancestors founded is quite rare. (These descendants must graduate from high school, graduate from college, want to attend law school, want to become a lawyer, and score well on the LSAT. The odds are remote. I can only imagine that there are a handful of people who have applied to a top law school being a direct descendent of the founder.)
Since, it is so rare, I think it is almost impossible for anyone to answer and I don't think you can get a factual answer with historical evidence on this board.
Do I think you have a good chance? I would say yes, but this is just a guess on my part.
Really, though I mean what is the question you have here? You take the LSAT, you pay the 80 bucks and apply, and see if they accept you. No one is going to tell you to do anything different here. There is nothing you can do but apply.