We have designed a proton beamline based on a rapid-cycling synchrotron for Flash radiation with ultra-high dose rate. Because proton beams can be extracted within hundreds of nanoseconds in the rapid-cycling synchrotron, its energy can be altered from one cycle to the next with different extraction time. The intended beamline system can achieve layer stacking irradiation at an instantaneous dose rate of 10⁷ Gy/s. Each longitudinal layer requires a different beam intensity. The target is divided longitudinally into different layers, each of which needs a different beam energy, to produce a uniform irradiation field. The system, including a double scatter system, a range compensator, a ripple filter, and a multi-leaf collimator to maximize proton fluence into the target, is simulated using the Monte Carlo software FLUKA. Three different kinds of ripple filters are built for the low, medium, and high energy zones based on the original Bragg peaks to reduce the number of energy layers and shorten the total irradiation duration. These filters transform the spike region into a Gaussian distribution with flat expansion areas of 2 cm, 6 cm, and 20 cm, respectively. Combining the rapid-cycling synchrotron with the layer stacking irradiation provides a novel method for achieving Flash proton irradiation, which delivers an ultra-high dose rate to the target.