I have a different take, but I'm also drawing from the few details you put in your original post. It sounded like you only had a simple website and some thoughts about what the company could be, and that's it. If that's the case, I would
not mention the startup in your materials as they would definitely have follow-up questions for you in an interview and it could sound like you just put "founded a startup" on your resume/app solely because you thought it would sound good/differentiate you. If you wouldn't have something significant to say about the company if you were peppered with questions in an interview, I would hesitate in advising you to include it on your app because they could view it as untruthful or deceptive.
However, if you've actually raised money, have a board/advisors, have some sales/clients lined up (even if you don't have any revenue), have a business plan out to some angel groups to review or have made presentations in front of such groups, etc., then you should DEFINITELY mention the experience in your app, and be sure to include those details. Without that sort of context, it may raise a few eyebrows.
Again, I'm only going by the assumptions I'm making from your original post. It wasn't clear what "founding a startup" actually meant (to you) in that post so I hope I interpreted your concern correctly.
Hope this helps!
Erika