As a criminologists who does a lot of research on and with police, it's just an incredibly complex issue. The chief is right that police are asked to do too much with too little, and there are a host of societal and legal problems intertwined that lead to many of the issues police and communities today face.
A big problem with the current tension, as many have noted, is there's too much all or nothing, us vs. them type stuff going on from both sides. If you're pro-black lives matter, you get viewed as anti-police. If you're pro-police you're anti-black people.
We should all be pro black lives matter and opposed to all the discrimination that happens in law enforcement and other areas of life. We should all also be supportive of police as most are good people, working to keep our communities safe and orderly, for relatively low pay in most places (especially big cities). And they're doing it with a lack of personel and resources after all the cuts to state and local budgets since 2008.
That said, police leaders need to step up and bring about the types of reforms needed that are in the realm of things they can change. They need to start taking cases of discrimination, illegal use of force, illegal stops and searches seriously. Promote whistleblowing, and appropriately discipline cops who abuse their powers and especially those who violate the law. Re-shape police training to address racism and prejudices. Spend more time training officers in how to deescalate situations, how to handle mentally ill persons and so forth. However, that requires money and resources. It's going to require either higher taxes or cuts to other areas of state and local budgets.
Beyond that, we need major changes to our legal system and society in general. We need to end the war on drugs and all the stops, frisks and searches that go along with it. None of this has worked, it's given too many non-violent individuals criminal records that make it very hard to turn one's life around with all the things having a felon record preclude you from. In general there's just too much overpolicing, too many arrests, too much incarceration. The system needs to be more focused on prevention and focusing arrests etc. on serious violent and property crime. More use of warnings and working with the community to deal with disorder problems, low level drug problems and so forth.
As for society in general, hopefully the rise of Trump and all his bigotry is a wake up call that racism, bigotry and discrimination are far from dead in this country. All aspects of social policy need to focus on promoting equality and diversity to counteract all the institutionalized racism, concentrated disadvantage in minority communities and all the other things that end up concentrating crime, and therefore police attention, in certain types of communities.
The police can do a lot more than they have to limit abuses of power and discrimination by officers. But that will be a drop in the bucket without fixing the larger problems in society that underlie the issue.