King used the segregation in the Holocaust just like during the civil rights movement.
Even though it's an extreme case, the treatments of jews during Holocaust was derived from the same perception that most American have before the civil rights. They believed that the racial minorities were inferior and should receive different treatment compared to the majority.
King was making this comparison to make people realize that it only took time before the different treatment keep escalating and in the end the same thing could happen to the minorities in united states.
