Robotic vehicles that are capable of autonomously transitioning between various terrains and fluids have received notable attention in the past decade due to their potential to navigate previously unexplored and/or unpredictable environments. Specifically, aerial-aquatic mobility will enable robots to operate in cluttered aquatic environments and carry out a variety of sensing tasks. One of the principal challenges in the development of such vehicles is that the transition from water to flight is a power-intensive process. At a small scale, this is made more difficult by the limitations of electromechanical actuation and the unfavorable scaling of the physics involved. This paper investigates the use of solid reactants as a combustion gas source for consecutive aquatic jump-gliding sequences. We present an untethered robot that is capable of multiple launches from the water surface and of transitioning from jetting to a glide. The power required for aquatic jump-gliding is obtained by reacting calcium carbide powder with the available environmental water to produce combustible acetylene gas, allowing the robot to rapidly reach flight speed from water. The 160-gram robot could achieve a flight distance of 26 meters using 0.2 gram of calcium carbide. Here, the combustion process, jetting phase, and glide were modeled numerically and compared with experimental results. Combustion pressure and inertial measurements were collected on board during flight, and the vehicle trajectory and speed were analyzed using external tracking data. The proposed propulsion approach offers a promising solution for future high-power density aerial-aquatic propulsion in robotics.