Granular flows often exhibit size segregation along both the depth and flow-directions, yet the mechanisms driving segregation in the flow-direction remain poorly resolved. Using three-dimensional discrete element simulations, two intrinsic flow-direction segregation mechanisms that operate independently of depth-direction stratification: forward kinetic sieving, in which smaller particles advance due to higher granular temperature and geometric mobility, and shear-induced migration, in which larger particles with stronger contact networks transmit shear more efficiently and move forward. These mechanisms are distinct from secondary forward advection, where large particles elevated into faster surface layers by depth-direction segregation are subsequently carried downslope. The dominance of flow-direction segregation is shown to depend on the temporal stage of depth-direction structuring: forward kinetic sieving prevails during early stratification, whereas shear-induced migration governs once depth segregation stabilizes. Based on these insights, a continuum framework is developed that, for the first time, couples depth-and flow-direction segregation into a unified model, demonstrating strong agreement with simulation results. The findings clarify the bidirectional interplay of granular segregation and improve predictive modeling of hazard-related granular flows.