Fractures play important role in unconventional resources by influencing the fluid flow pattern underground. Streamline-based flow diagnostic is important to the history matching or operational optimization process of fractured reservoirs. This paper presents a robust streamline tracing framework for use in the Embedded Discrete Fracture Models (EDFM) and several applications including flow visualization, flow diagnostics, and rate allocation optimization. The proposed streamline tracing framework is based on a boundary layer method that can honor the flux communications between the matrix and fractures or between fracture and fracture. The proposed method is benchmarked with a semi-analytical solution and its robustness is illustrated by a series of numerical examples encompassing different levels of geologic and geometrical complexity. Streamlines in complex fracture networks provide flow diagnostics such as sweep efficiency and connectivity of wells and fractures. The streamlines are then utilized to develop a workflow for rate allocation optimization for waterflood in naturally fractured reservoirs. We apply a streamline-based gradient free algorithm whereby both injection and production rates are adjusted under realistic operational constraints to a field scale fractured reservoir. This approach only requires a few forward simulations and therefore offers significant advantage in terms of computational efficiency. It is confirmed that the optimized schedule provides improvements in oil recovery and sweep efficiency compared to the base scenario with uniform injection and production rates.