No, unfortunately not.
In the Supreme Court ruling, the Court specifically addressed the issue that the purpose for which the information was shared was relevant to the establishment of a privacy interest.
Cell phone information is shared with the cell tower operators as a necessary function of the cellular system: your phone wont work if the towers do not know how to route the data to you. You maintain a 4th amendment privacy interest in the information, even though it is shared with third parties.
Your license plate number is shared for the purpose of identifying your vehicle to police/government authorities. You do not have a 4th amendment privacy interest in keeping it from the police/government authorities.
We will have to find other ways of getting Flock out of our lives. It will probably take passing new laws to do it.