Simulating multiphase flow in highly fractured porous media, such as in oil reservoirs with complex geological heterogeneities, presents significant challenges for traditional computational methods. In this work, we present a multiscale approach for the fast prediction of multiphase flow, combining high-fidelity simulations with a data-driven strategy. A key innovation is the novel characterization of the fracture network geometry, which is crucial for accurate flow prediction in fractured reservoirs. The local intrinsic permeability tensor is homogenized using representative volume element (RVE) simulations that account for embedded fractures. The results from these fine-scale RVE simulations are then used to train machine learning-based surrogate models, which are subsequently employed in global-scale simulations solved on coarse meshes. This multiscale pseudo-direct numerical simulation (P-DNS) method is applied to single-phase and two-phase flow problems in 2D manufactured cases, designed to represent typical reservoir scenarios. We demonstrate that the P-DNS approach provides accurate flow rates and pressure fields on coarser meshes, achieving computational speedups of up to a factor of 500 compared to high-fidelity simulations. This work highlights the potential of combining multiscale methods and machine learning for fast and accurate simulations of complex flow dynamics in fractured porous media, offering a powerful tool for practical reservoir simulations and related applications.