I am not a lawyer, but I have questions as to whether the driver's actions qualified as Flight From An Officer (as defined by Louisiana R.S. 14:108.1) and whether the attempted stop was reasonable to begin with.
To start with, LRS 14:108.1 provides that an officer must have reasonable grounds to believe the driver committed an offense. In this case, the deputy was the one who misread the license plate. A mistake made by an officer does not equal an offense committed by a driver, thus I believe the deputy did not have sufficient legal authority to stop them in the first place.
LRS 14:108.1 also provides that an officer must be using both visual and audible signals (emergency lights AND siren). In this case, the deputy did not activate his siren until his supervisor mentioned it, after which the driver pulled over and stopped once she found a safe place to do so.
With the preceding information in mind, it does not appear to me that the driver's actions legally amount to the crime of Flight From An Officer, and it appears to me that the deputies did not have sufficient legal authority to charge her with such. Furthermore, because I do not believe the deputy had sufficient legal authority to make a traffic stop to begin with, it does not appear to me that they had sufficient legal authority to search the vehicle and charge all four occupants with drug possession either.
Again, I am not a lawyer, but I personally think those people should sue.