What are the qualities described by Martin Luther King of the ''veteran of creative suffering?''

The line you are asking about is from one of the most powerful speeches ever delivered in the United States:  Martin Luther King's "I Have a Dream" speech. The chief quality that the "veteran of creative suffering" possesses is the experience of enduring great injustices in the United States, purely for being of a different race. The specific qualities mentioned by King are found in the sentences preceding his description of African-Americans as veterans of creative suffering.  

"I am not unmindful that some of you have come here out of great trials and tribulations. Some of you have come fresh from narrow jail cells. And some of you have come from areas where your quest -- 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." --Martin Luther King

In this passage, King describes the violent treatment of black people at the hands of law enforcement.  He describes how his people are being jailed for protesting against their oppressive treatment.  King was jailed on numerous occasions and was a veteran of this suffering himself.  

The paragraph before this also describes the lack of economic and political opportunities for black Americans.  It speaks of segregation at hotels and the condition of the ghettos.  These are also qualities of "creative suffering."

"We can never be satisfied as long as our bodies, heavy with the fatigue of travel, cannot gain lodging in the motels of the highways and the hotels of the cities.  We cannot be satisfied as long as the negro's basic mobility is from a smaller ghetto to a larger one. We can never be satisfied as long as our children are stripped of their self-hood and robbed of their dignity by signs stating: "For Whites Only."  We cannot be satisfied as long as a Negro in Mississippi cannot vote and a Negro in New York believes he has nothing for which to vote. No, no, we are not satisfied, and we will not be satisfied until "justice rolls down like waters, and righteousness like a mighty stream." --Martin Luther King