Using numerical simulations, we study the gravity driven flow of jammed soft disks in confined channels. We demonstrate that confinement results in increasing the yield threshold for the Poiseuille flow, in contrast to the planar Couette flow. By solving a nonlocal flow model for such systems, we show that this effect is due to the correlated dynamics responsible for flow, coupled with the stress heterogeneity imposed for the Poiseuille flow. We also observe that with increasing confinement, the cooperative nature of the flow results in increasing intermittent behavior. Our studies indicate that such features are generic properties of a wide variety of jammed materials.