Focused fluid flow through sub-seafloor pipes and chimneys, and their seafloor manifestations as pockmarks, are ubiquitous. However, the dynamics of flow localization and evolution of fluid escape structures remain poorly understood. Models based on geomechanical mechanisms like hydro-fracturing and porosity wave propagation offer some useful insights into fluid flow and escape dynamics, but face limitations in capturing features like mobilized granular matter, especially in the upper sediment layers where the link between fracture and pockmark is not always clear. Here, we propose a mathematical model based on the multiphase theory of porous media, where changes in subsurface and seafloor morphology are resolved through seepage-induced erosion, fluidization, transport, and re-deposition of granular material. Through simulation of an idealized scenario of gas escape from overpressured shallow gas reservoir, we demonstrate that our model can capture flow localization and formation of pipes, chimneys, and pockmarks. Our simulations show (1) formation of conical focused-flow conduits with a brecciated core and annular gas channels; (2) pockmarks of W and ring shapes; and (3) pulsed release of gas. Sediment erodibility and flow anisotropy control the morphology of focused fluid flow and escape structures, while permeability shows negligible impact. While the geological setting for this study is theoretical, we show that our results have real-world analogs.