To find the meaning of this phrase, look at the parts of the speech just before this line. You can see the meaning in the whole paragraph that contains the line.
King clearly does not mean that he thinks that black people are created differently. He was a man who believed in the equality of all people.
It is closer to say that he is talking about the suffering associated with creative work. In this paragraph, he talks about how many of the people at the rally had come there from jail cells and such. So what he is saying is that they have suffered (legally and physically) as they have been trying to create a more just society. He is acknowledging how they have suffered to try to achieve the goals of their movement.
Here is the rest of the paragraph -- you will see that it supports my interpretation
Some of you have come fresh from narrow jail cells. Some of you have come from areas where your quest for freedom left you battered by the storms of persecution and staggered by the winds of police brutality. You have been the veterans of creative suffering.