The local flow field and swimming motility of a choanoflagellate model is presented. The method of regularized Stokeslets is used to simulate the interactions between the elastic 2D model of a single choanoflagellate and the surrounding fluid. We use experimental data to build the model with three parts (cell body, flagellum and microvilli), and then vary the parameters to find the optimal swimming speed of the flagellum. Our simulations show how vortex flow forms due to the motion of the flagellum. We also examine the trajectories of fluid particles close to the organism. We explore how local flow fields change when we add the microvilli into the model. Depending on the angle and the length of microvilli, the fluid particles might move in different directions. We can extend our model to 3D because the fundamental methods are the same. Based on our work, one can further investigate the interactions between two or more choanoflagellate models or explain local flow fields around a colony.