Just a side note: I would characterize those cases in the exactly opposite way. The evidence suggests plainly that Wilson was legally authorized to use lethal force. On the other hand, Garner's treatment was ludicrous and inexplicable.
As for the question above, no, BLM the movement is not responsible for cop-killing. Obviously. Deray M. and the other prominent protesters (along with their thronged masses of acolytes), buffoons and idiots though they are, are not calling for violence. It isn't libertarianism's fault when a nut blows up a federal building, and it isn't BLM's fault when a nut shoots a police officer (or when a couple dozen nuts chant a perversion of that the vast majority of the crowd is chanting).
More generally, BLM is what all these kinds of thing are these days: a group finds a worthy (though still reductive/incomplete) cause, builds a narrative, begins granting the narrative preference over fact and reality, veers into fantasyland and idiocy.
"Reductive" is the operate word in this post. BLM's first flaw, from which all the other ones emanate, is in its ludicrously reductive and misleading assessment of anecdote and data.