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.