We study the quantum sheaf cohomology of flag manifolds with deformations of the
tangent bundle and use the ring structure to derive how the deformation transforms under
the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted twodimensional theories with (0,2) supersymmetry, quantum sheaf cohomology generalizes the
notion of quantum cohomology. Complete descriptions of quantum sheaf cohomology have
been obtained for abelian gauged linear sigma models (GLSMs) and for nonabelian GLSMs
describing Grassmannians. In this paper we continue to explore the quantum sheaf cohomology of nonabelian theories. We first propose a method to compute the generating relations
for (0,2) GLSMs with (2,2) locus. We apply this method to derive the quantum sheaf cohomology of products of Grassmannians and flag manifolds. The dual deformation associated
with the biholomorphic duality gives rise to an explicit IR duality of two A/2-twisted (0,2)
gauge theories.