In obstacle-dense scenarios, providing safe guidance for mobile robots is critical to improve the safe maneuvering capability. However, the guidance provided by standard guiding vector fields (GVFs) may limit the motion capability due to the improper curvature of the integral curve when traversing obstacles. On the other hand, robotic system dynamics are often time-varying, uncertain, and even unknown during the motion planning process. Therefore, many existing kinodynamic motion planning methods could not achieve satisfactory reliability in guaranteeing safety. To address these challenges, we propose a two-level Vector Field-guided Learning Predictive Control (VF-LPC) approach that improves safe maneuverability. The first level, the guiding level, generates safe desired trajectories using the designed kinodynamic GVF, enabling safe motion in obstacle-dense environments. The second level, the Integrated Motion Planning and Control (IMPC) level, first uses a deep Koopman operator to learn a nominal dynamics model offline and then updates the model uncertainties online using sparse Gaussian processes (GPs). The learned dynamics and a game-based safe barrier function are then incorporated into the LPC framework to generate near-optimal planning solutions. Extensive simulations and real-world experiments were conducted on quadrotor unmanned aerial vehicles and unmanned ground vehicles, demonstrating that VF-LPC enables robots to maneuver safely.