W. E. B. DuBois and Ta-Nehisi Coates, though a century apart, would have much to say to each other because both had similar experiences of racism.
As for DuBois's response to the Coates's concept of "the Dream," first we need to describe the Dream. Coates characterizes it as a White person's construct of an ideal society. He describes it as
perfect houses with nice lawns. It is Memorial Day cookouts, block associations, and driveways. The Dream is treehouses and the Cub Scouts. The Dream smells like peppermint but tastes like strawberry shortcake.
What he describes is often referred to as the American Dream, but Coates refuses that label because it is, he says, only a dream for some Americans. It is a White dream built on the labor of Black people and depends on excluding Black bodies.
In the conversation, DuBois would likely point out that "the Dream" is an updated version of his concept of the "veil," articulated in his classic 1900 work The Souls of Black Folk. DuBois would explain that in that book he speaks, much as Coates does in his own work, of feeling excluded from White society. Du Bois describes it as being
shut out from their world by a vast veil.
Black people, DuBois would state, are perceived as a "problem" by White society. This is because White people look at Black people differently than Black people look at themselves. DuBois would explain to Coates that he calls these two different perception the "double consciousness:"
this sense of always looking at one’s self through the eyes of others, of measuring one’s soul by the tape of a world that looks on in amused contempt and pity
We can imagine DuBois sharing with Coates a sense of frustration that Black integration and inclusion have improved so little in the more than a century since DuBois wrote The Souls of Blacks Folk. Coates would identify with the concept of double consciousness because he too writes of having to have an awareness of his Blackness at all times and of the danger being Black poses for him and other Black males.