Since a shine can be jump-cancelled, it can be chained into any jump-cancelled technique, including Jump cancel shine.
Double shines are most commonly used as part of shield pressure, since they beat Shine out-of-shield; Falco's more readily than Fox's.
In the corner, they can also send an opponent far offstage and set up for an edgeguard. Actually hitting with both shines takes good execution; it's much easier with momentum.