The Kuiper belt is one of the last mostly unexplored regions in the Solar System. Exploration of the Kuiper belt can greatly increase humanity's understanding of the Solar System's formation and evolution. The use of low-thrust propulsion for Kuiper belt missions has the potential to improve the payload mass of the mission due to the high efficiency of its propellant. This research looks at the required methodology to optimize low-thrust trajectories with Kuiper belt object flybys. The trajectory is modelled using Tudat with spherical shaping as the trajectory parameterization method. A methodology is constructed which switches between high-thrust and low-thrust legs to constrain the input space for the low-thrust optimization problem. By using close-approach graphs and optimizing multiple flybys at the same time a trajectory with two Kuiper belt object flybys is found. The result is a robust method to find Kuiper belt object flyby trajectories with low-thrust propulsion.