I've often thought of making a mobile app that securely uploads a video in real time to a secure server, out of the reach of law enforcement. That way, physical possession of the phone is irrelevant if law enforcement gets its hands on it. Alas, almost every online search brings up info for live streaming to an iOS device, not streaming from one (and I think it'd be quite a challenge).

TLDR basically Periscope, but in a way that the uploaded video is encrypted and the cops can't access it.