The earth's population is growing at a rapid rate, while the availability of water resources remains limited. Water is required for various purposes, including drinking, agriculture, industry, recreation, and development. Accurate forecasting of river flows can have a significant economic impact, particularly in agricultural water management and planning during water resource scarcity. Developing precise river flow forecasting models can greatly improve the management of water resources in many countries. In this study, we propose a two-phase model for predicting the flow of the Blackwater river located in the South Central United States. In the first phase, we use Multigene Symbolic Regression Genetic Programming (MG-GP) to develop a mathematical model. In the second phase, Particle Swarm Optimization (PSO) is employed to fine-tune the model parameters. Fine-tuning the MG-GP parameters improves the prediction accuracy of the model. The newly fine-tuned model exhibits 96% and 94% accuracy in training and testing cases, respectively.