In an idealized representative democracy, the appropriate civilian response to police misconduct is voting. In all cases, the people who set agendas for community policing — mayors, county sheriffs, police chiefs, etc — are either elected directly or are appointed by elected officials. Getting a sympathetic elected official into office, thus, would automatically change the agendas of the police. It might take some time for new agendas to sink down through the ranks, because police (like any other organized group) have their own internal culture, practices, and interests. A police veteran on the streets might resent being told to change practices and habits that have kept him alive over years of service, particularly if it comes from some 'politician'. But power ultimately rests in elected offices, and with persistence change would come.
Of course, the US implementation of representative democracy is far from ideal. Voters are often under-informed and confused; elected officials often respond more to powerful special interests than community concerns; police culture is often solidified through powerful unions, codes of silence, rejections of oversight and transparency, and other 'blue line', us vs. them attitudes. Where voting proves ineffective in changing police behavior, public exposure becomes the next best option. Peaceful protests, journalistic investigation, and social media coverage are all effective ways to bring public attention to improper actions, and sufficient attention of this sort can often induce corrective action or collective shame: the first to re-moralize both elected officials and active police officers; the second to demoralize officials and officers who refuse to respond. The people involved may not be responding for the right reasons — i.e., they may be trying to scratch a public itch rather than pursue a properly moral course — but in the end results are what matter.
If neither voting nor peaceable exposure has any effect, well... As Clausewitz said, "War is the continuation of politics by other means," and this is true of violence of all sorts. I cannot condone rioting, looting, or arson, but I can certainly understand that someone who cannot make himself heard when he speaks quietly, calmly, and civilly might reasonably begin to shout. Representative democracy only works when people in power listen and hear. If the powerful refuse to listen and refuse to hear, then I cannot entirely blame citizens for turning up the volume through violent acts. That is a natural (if undesirable) effect.
Police have a difficult job. They are called upon by citizens to control citizens who misbehave, and this sometimes forces police to take actions that most citizens would be squeamish about. Police are authorized to use violence against citizens because sometimes they must use violence against citizens, to protect themselves and the larger community. But because police are granted that authority, they are implicitly held to a higher standard of behavior. Given that individual officers are as fallible as anyone else in the population, the political question centers on who will hold police officers to that higher standard? Who polices the police? If elected officials won't do it then the police must do it themselves; if the police won't do it, the the public must take up the reins. Hopefully we can find some political means for the public to take up the reins of the police that falls far short of burning down police stations, but that is something that police and elected officials must embrace. If they are merely set on suppressing protests, violence will only escalate.