But is it not the government hiring flock to do this?
That largely depends on what the contract actually says, and how the data is 'federated' within Flock's own systems.
It sounds like Flock's business model was to build the massive data-collection system, but since that's expensive, it used contracts with government entities to pay for the build-out. The contracts with each of the entities might well be for the services delivered to them, but since many municipalities have separate contracts for how real estate (and installing something on a light pole counts) then Flock might be maintaining their own contracts separately for the physical placement of their cameras.
So Flock gets agencies/government to pay for the services of license plate data collection with one contract then uses another contract for Flock to pay for the rental for pole space. If the contract to provide data to the polity lapses or is terminated, that doesn't necessarily mean that Flock's permits to maintain equipment on poles is also terminated as they're separate contracts. Granted, operating the cameras is on Flock's dime now, but if they continue to harvest data then they might find takers for that data even if not the original municipality or other agency who paid for the cameras.
The thing that our current interpretation of the Constitution lacks is where the dividing line between one's self and a third-party sits when it comes to the sanctity of one's person, papers, and effects. At the time that the Constitution was written there was no photography, let alone videography, mass-processing of records automatically, etc. Someone had to physically observe someone in public in order to know what they did, and could only repeat with their words what they saw rather than demonstrating it. We don't have good law for 3rd party collection of volumes of data about people and the ability of said 3rd party to provide that data to the government. A ruling, law, or amendment that puts protections on requesting information and establishes some kind of checks and balances system that applies to the government in all its forms is needed. I don't know what the threshold should be either, but clearly right now when we have stories where the justification for a search is, "ASDFG" then something needs to change.