The join of two graphs G and H is a graph formed from disjoint copies of G and H by connecting each vertex of G to each vertex of H. We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero 3-flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus an isolated vertex joined with a graph containing only isolated vertices, and two isolated vertices joined with exactly one isolated vertex plus some number of isolated edges.