We propose a novel Model Predictive Control (MPC) framework for a jet-powered flying humanoid robot. The controller is based on a linearised centroidal momentum model to represent the flight dynamics, augmented with a second-order nonlinear model to explicitly account for the slow and nonlinear dynamics of jet propulsion. A key contribution is the introduction of a multi-rate MPC formulation that handles the different actuation rates of the robot's joints and jet engines while embedding the jet dynamics directly into the predictive model. We validated the framework using the jet-powered humanoid robot iRonCub, performing simulations in Mujoco; the simulation results demonstrate the robot's ability to recover from external disturbances and perform stable, non-abrupt flight manoeuvres, validating the effectiveness of the proposed approach.