Should I leave a gap between clay bricks when laying a patio?
Yes, you should leave a small gap, but not for the reasons you are asking. 

You will be concerned with evenness. Reclaimed bricks won't have a chamfer on the edges the way paving bricks will, so small differences in your sand bed will be very noticeable to feet and patio furniture. 

Your gap size will be mostly aesthetic, but wider gaps will make your bricks less stable. To space it, just use anything that is the right size, e.g. scrap wood or screws, and fill in your joints every few feet.