An order-order transition from a bicontinious double-gyroid (G) structure to a hexagonally packed cylinder (C) structure induced by an external flow is simulated by using real-space dynamical self-consistent field technique. To simulate the structural change correctly, we introduce a system size optimization technique by which emergence of artificial intermediate structures are suppressed. When a shear flow in [I I I] direction of the G unit cell is imposed, a nucleation of the C domains followed by a stable coexistence between the G phase and the C phase is observed. We confirm that the generated C domains grow epitaxially, where the {220} planes of the G structure coincide with the {10} planes of the C structure (so-called epitaxial growth), while the experimental studies suggest {211} to {10} transition. In a steady state under the shear flow, the G structure shows different splitting and reconnection processes when the direction of the velocity gradient of the shear flow is changed. Thus, the kinetic pathway from the initial G phase to the final C phase is determined, not only by the commensurability between the positions and the lattice constants of the initial and the final domain structures (epitaxial condition), but also by the stability of the phase coexistence that depends on the direction of the velocity gradient.