"Who is responsibile for avoiding a kick, the rider of the kicking horse or the intended target?"
The answer is that it`s a shared responsibility, both parties have a duty toward each other. I`ll try to keep this short but it`s a tough subject... Also I need to drop a standard disclaimer: contact your personal attorney if you want specific legal advice, the discussion which follows is from my view as a fellow endurance rider.
There is a concept in the law called comparitive negligence. The acts of both the tort feasor (rider of the kicking horse) and the injured party are evaluated by the court or a jury. Then the percentage of tort-feasor responsibility is multiplied by the amount of the damages to determine the award.
However, many states have adopted a "modified 51% bar against negligence claims." Under this system if the tort feasor is not responsible for 51% or more of the cause of the injury, then no cause of action is deemed to exist. Stated differently, the defendant must be more responsible for the act(s) giving rise to the damages than the claimant.
Now the pop-quiz: Can you think of any endurance-related situations where the 51% rule might apply?
So back to your specific question... there are three additional topics related to your concern about libility worth mentioning:
First, have you given fair warning? A red flag you mention is a practice widely accepted in our sport and usually gives fair warning assuming one can see it. The down side to the red flag is that it also indicates that you know she has a propensity to kick. Thus a red flag also means that you have a higher level of duty towards other riders than one riding a horse that has never kicked at a ride. You must ride in a manner which minimizes the risk to others (not a bad idea for all of us).
Second, have you and/or your fellow riders assumed the risk of being kicked? Signing a liability release does not normally change the duty relationship between competitiors. This is because such releases often do not mention competitior-to- competitor liability. Also, when one signs a release there are certain unstated assumptions called "industry practices" Namely, that all competitiors will act reasonably in the context of competition (i.e. not trying to shove you over as they pass on a narrow trail.) An grossly unreasonable act may give rise to liability even though a release has been signed.
Third, does your state have an equine liability limiting law? As Bob mentioned in a prior post, many states have adopted statutes limiting the types of suits that may be brought as a result of an equine-related injury. BUT, and this is important, most of these laws allow claims for injuries caused by intentional acts. In this context, an intentional act can also be a "purposeful failure to act." This is called an "omission" and means failing to act when there was a duty to do so. So if one says, "if they try to pass, whatever happens is not my fault" and then makes no attempt to prevent the injury, a suit for resulting damages may be allowed.
In summary, every dangerous horse incident is "fact-specific." It`s almost impossible to generalize whether one would be liable if "X" occurs. The key to avoiding problems is to ride defensively and try to avoid incidents which may lead to problems.