You asked how much torques is required to spin up the flywheel  this has absolutely nothing to do with what type of engine is used to create that torque.
The equation that governs torque and angular acceleration is T= I alpha, where T= torque applied, I = moment of inertia, and alpha = angular acceleration in radians per second squared. The angular acceleration here is equal to the final angular velocity (in rad/s) divided by the time it takes to reach that velocity. The final angular velocity in radians/second is 1500 RPM x 2 pi radian/rev x 1 min/60 sec. The only remaining trick to consider is that the value of 'I' that you gave is in lb_mass  ft^2, and once you do the math you will end up with torque in units of lb_mass  ft^2/s^2, which you will then have to convert to lb_force  ft by using the conversion 1 lb_force = 32.2 lb_m ft/s^2. I'll leave the math to you, but I suggest after you work this through you post back with your final result, and we'll be glad to check it for you.
