Clone Stamp duration

You can set the duration in the Paint panel. The Paint workspace arranges the Comp/Layer/and Paint panels so the controls are easy to reach. 

When you have created a clone stamp or any Paint stroke, selecting the layer and pressing the U key twice will reveal the length of the clone stamp (stroke), show you the path, allow you to change the timing, set keyframes, and adjust other parameters. It's not a very handy UI, but it can be useful for fixing some problems and adjusting the animation's timing. Revealing all of the Layer/Effects/Clone/Stroke options will give you a lot of other properties you can animate and adjust. 

You can even create a shape layer path with the pen tool, drag a pickwhip from the Clone/Path to the Shape Layer/Contents/Shape Path, and then animate the shape layer path in the Composition Panel to have the clone brush follow the same path as the shape layer.