Idea: A Universal Flag System, since HIPPA laws really prevent showing a mental health condition in a background check, A Universal Flag could be registered in their name, it’s universal so the same flag would be used for felons, so it wouldn’t out someone’s mental health history and violate HIPPA or their 4th amendment rights.

But this already exists. The NICS system simply flags people as yes/no for any reason handed down by a court, including mental illness at the testimony of a relevant medical professional. The only thing you're doing different from what already exists is removing the need for a court, meaning removing the need for burden of proof, meaning you're doing nothing to improve safety and simply making it easier for false accusations to be used to remove a right. No.