Mesoscopic simulations of hydrocarbon flow in source shales are challenging, in part due to the heterogeneous shale pores with sizes ranging from a few nanometers to a few micrometers. Additionally, the sub-continuum fluid-fluid and fluid-solid interactions in nano- to micro-scale shale pores, which are physically and chemically sophisticated, must be captured. To address those challenges, we present a GPU-accelerated package for simulation of flow in nano- to micro-pore networks with a many-body dissipative particle dynamics (mDPD) mesoscale model. Based on a fully distributed parallel paradigm, the code offloads all intensive workloads on GPUs. Other advancements, such as smart particle packing and no-slip boundary condition in complex pore geometries, are also implemented for the construction and the simulation of the realistic shale pores from 3D nanometer-resolution stack images. Our code is validated for accuracy and compared against the CPU counterpart for speedup. In our benchmark tests, the code delivers nearly perfect strong scaling and weak scaling (with up to 512 million particles) on up to 512 K20X GPUs on Oak Ridge National Laboratorys (ORNL) Titan supercomputer. Moreover, a single-GPU benchmark on ORNLs SummitDev and IBMs AC922 suggests that the host-to-device NVLink can boost performance over PCIe by a remarkable 40%. Lastly, we demonstrate, through a flow simulation in realistic shale pores, that the CPU counterpart requires 840 Power9 cores to rival the performance delivered by our package with four V100 GPUs on ORNLs Summit architecture. This simulation package enables quick-turnaround and high-throughput mesoscopic numerical simulations for investigating complex flow phenomena in nano- to micro-porous rocks with realistic pore geometries.