They need to be very careful that they write any such law so that people don't fear they will be punished or their loved one will be punished for reporting mental health issues. It is already very difficult to get people to report these things but if it results in them being officially red flagged by the government it could have real long term implications both on the ability to get people to report and the people who are flagged.
For these flags to be affective their has to be a way to access them. If they can be accessed employers law enforcement can and will use that information. This will scare people away from reporting and seeking help. Mass shooting gets big headlines but it isn't as deadly or destructive as unreported mental health issues.