As others remarked, the riots are puzzling to us adults as well — that's the reason you are asking. We are struggling to explain it not because there is a truth so terrible that it is unsuited for children; it's rather that it seems morally wrong and not conducive to the eventual goal of achieving racial justice. So why are people rioting and looting anyway?
One answer is that we humans don't always act rationally, and don't always act morally. I'm sure that you can find general examples for that in something your children did: They lashed out to somebody out of frustration, or did something they were not supposed to do because an opportunity presented itself.
But without addressing the underlying social reasons the picture would not be complete: Where does the frustration come from? Why specifically looting?
I personally think that it can be explained, also to a 6 year old, by the structural injustice simmering. Note that I'm not handing out a moral judgement here — rather, I'm observing.
Wages have, since the 1970s, not risen with the economic growth the way they used to before.1 The resulting prosperity has gone to very few who live in a state of unreal wealth that used to be reserved for kings and queens. Many normal people feel they don't have a chance to ever get their hands on one of the Dolce & Gabbana bags at display in the stores on 5th Avenue. And yet they are presented in the store windows almost as if intentionally mocking and teasing: "See, here I am, an arm's length away, but you'll never get me. I am here not for you, I'm here for the others." It's not surprising that in a moment of emotional upheaval, in an excited crowd, feeling short-changed all the way, without any fear of being punished for it, people grab what they can get. I can also see why the looters may not have that much of a bad conscience.
You can explain racism and systemic economic short-changing by an example. If you were systematically unfair to one of your children (I think you have more than one), the way the stepmother is in fairy tales; if you always would excludeexcluded the same sibling from nice clothes, dessert, cuddling, give them less pocket money etc. In a word, if you were systematicallsystematically discriminating against one of your childrensibling — how would that make them feel? Could they imagine to lose it if once again they don't get a present on Christmas while the other sibling plays with their new Xbox? Maybe they would take some of the sibling's toys away and hide them? Maybe they would even throw a tantrum and knock the Xbox off the shelf?? I think children are perfectly able to understand such a situation.
1 [This archived chart](https://archive.nytimes.com/www.nytimes.com/imagepages/2011/09/04/opinion/04reich-graphic.html) from the New York Times in 2011 shows that development.