Coupling flow with geomechanical processes at the pore scale in fractured rocks is essential in understanding the macroscopic fluid flow processes of interest, such as geothermal energy extraction, CO2 sequestration, and hydrocarbon production from naturally and hydraulically fractured reservoirs. To investigate the microscopic (pore-scale) phenomena, we present a fully coupled mathematical formulation of fluid flow and geomechanical deformation to model the fluid flow in fractured rocks. In this work, we employ a Darcy-Brinkman-Biot approach to describe the fully coupled flow and geomechanical processes in fractured rocks at the pore scale. Darcy-Brinkman-Stokes (DBS) model is used to model multi-scale flow in the fractured rocks, in which fracture flow is described by Navier-Stokes equations and flow in the surrounding matrix is modeled by Darcy's law. With this approach, a unified conservation equation for flow in both media (fracture and matrix) is applied. We then apply Biot's poroelasticity theory and Terzaghi's effective stress theory to capture the geomechanical deformation. The continuity of the fluid pressure is imposed to connect the DBS equation and the stress-seepage equation. This coupled model is employed to determine the permeability within the microfracture. Numerical results show that this coupled approach can capture the permeability under the effects of solid deformation and multi-scale formation. We develop a fully coupled model to capture the pore-scale flow-geomechanically process in fractured rocks. To our knowledge, the fully coupled framework is developed and applied to characterize fracture permeability at the pore scale in fractured rocks for the first time.