There’s an argument that a private citizen operating a Flock-like device is exercising a constitutionally protected right to gather news and observe public events, and sharing those observations is constitutionally protected free speech. And, unfortunately, the Fourth Amendment is worded to restrict government invasion of privacy, not citizen invasion of privacy.
I expect the Supreme Court to eventually rule on the constitutionality of mass surveillance of public places, at least by the government. Maybe also by random citizens.