The main thing that King is inferring about African American progress in entering main stream American life is that that progress could be accelerated through massive effort.
In his speech, King is saying that he has a dream of social progress. He has a dream that one day there will be racial harmony. This means that he has inferred that it is possible for things to change. The lack of integration that existed in his day was not something that was immutable. Instead, he inferred that it could change and he called for people to devote themselves to making that happen.