Strong, flexible glues, specifically adhesives containing vinyl acetate or rubber cement, are best when working with leather. Vinyl adhesive is most effective due to its versatility. It can be applied easily with a brush, thinned with water and dries clear.
When using glue with leather, apply the adhesive to both surfaces and leave it untouched until the color of the adhesive begins to change from white to clear and the surface becomes tacky. After pressing the two layers together, apply weights or clips, padded to protect the leather from marring. Before it dries, rub the edges to remove any obvious glue lines.