How did Martin Luther King Jr use conflict in order to affect change in Civil Rights? (Give examples)
As mentioned above Martin Luther King Jr used nonviolence often to provoke violence from the other side.
The Montgomery Bus boycott is the first example of King's use of civil disobedience and conflict that ensued as a result. Much of the civil disobedience that went on at lunch counters and post offices and on public transportation across the south was a result of what southern blacks and whites saw happen in Montgomery.
King led the Southern Christian Leadership Conference (SCLC) to continue with their acts of nonviolence and civil disobedience. The march on Washington was in some ways the culmination of his and his group's desire to put civil rights in the face of all Americans. Ultimately he knew that he had to raise awareness and tempers if he was going to create change. While he believed in nonviolence, there also is an understanding that nonviolence doesn't mean lack of conflict.
It could also be argued that he used people like Malcolm X to stir up the issue without being directly involved. Perhaps King did not actively recruit Malcolm X, perhaps he did. Either way, Malcolm X had the same goal, but markedly different means to get there. He did not have qualms about using violent conflict to make his point about racism and inequality.
You might find it useful to study or analyse how Martin Luther King used the approach of non-violent resistance that Ghandi used to such devastating effect in India. Both deliberately provoked armed conflict by non-violent protest to highlight the inhumanity of, respectively, racism in the USA and colonialism during the British Raj of India.
Martin Luther King used conflict, in the form of civil disobedience, to affect change in the laws governing civil rights in America.
King's main strategy in the Civil Rights Movement was to use conflict (albeit nonviolent conflict) to achieve the goals of the movement. He wanted to use conflict to get the attention of people in the North who might not otherwise care about Southern blacks. He also wanted to use conflict to highlight the moral differences between the protestors and the laws.
A perfect example of this can be seen in the protests in Birmingham, Alabama. These protests are the source of the pictures you see of demonstrators being sprayed with fire hoses and attacked by police dogs. By provoking this sort of conflict, King was able to get most of the US on his side. The conflict got people's attention and emphasized to them that the protestors had morality and American values on their side.