Conveyors are a standard application for gearmotors. You can educate yourself by getting the free catalogs & engineering guides from gearmotor manufacturers. The formulas should give you a good guide how to calculate torque requirements. You will also have to estimate how much material mass is being moved by the slats, gravity effects if any, etc etc etc. I know SEW Eurodrive has an online calculator in which one of the standard models is a generalized conveyor. Perhaps you can adapt it to your needs.
You can also learn by going back to the first principles of your engineering training (I take it you are a trained engineer?) and applying basic friction theory, then following it up with basic power calculations.
