The pragmatist doesn't think "We don't know if what we believe is true." The pragmatist does not think that "Our knowledge is flawed." I should say empiricism: underlying pragmatism is the view that we are traveling in a tree of branching possibilities. At any fork, our choice is based on the pragmatics of various factors that are entirely contingent. Necessarily we cannot know what life would be like at other nodes precluded by our past actions. And by all past events, for that matter. For these principles apply for all change, including our transformations as cultures, tribes and ethnicities and beyond that as species, and not just the evolution of our way of representing the world to ourselves (or of doing something functionally equivalent to that).
Against the Escher-like background of modality (the universe of possible worlds), the correspondence theory of truth looks incoherent: only the most general truths, the ones true at all possible worlds, can be said to "correspond to reality" in any literal way, and these (maybe, "there is a type of atom formed of one neutron, one electron, and one proton"? I don't know) will be important but inevitably esoteric, whereas virtually all of our run-of-the-mill claims (including the vast majority of "scientific" claims) have nothing to do with representing the world at all but are, rather, simply manifestations of the way we ourselves are: our bodies, our environments.
So work out this relationship between pragmatism and modality, through the connection of empiricism's law of effect. The argument is not that something that could be known is not known. The argument is that this concept of "knowledge" is wrong.