If you use a Date Time item type for the items it will show the timestamps on the items.
If you tap the clock in the top right, it will show the Time Out and Time In and Elapsed Time.
It supports one Time Out / Time In for the checklist. For more custom capability you would need to learn Value Triggers and some scripting to pull off. With scripting you could do very advanced things like save data in variables, do calculations and change the labels of content dynamically.