Abstract: In this talk we present a new correspondence for pairs $(\mathbb,H)$ formed by a flag manifold $\mathbb$ together with an $H$-flux on $\mathbb$. Given its role within our correspondence, infinitesimal $T$-duality may be viewed as a source of $H$-flux, in the sense that it contributes towards taking fluxless pairs $(\mathbb,0)$ to pairs $(\mathbb^\vee, H^\vee)$ carrying nontrivial flux $H^\vee\neq 0$. We also illustrate how our correspondence exchanges complex structures with symplectic ones up to $B$-transformations. This is a joint work with Elizabeth Gasparim and Lino Grama.