Many backsplashes match labradorite, and the best one depends on the look you like. For an easy option, use Labradorite as your backsplash. Another idea is a glass backsplash that pulls color from the stone. (I.E., if your counter has blue flashes, use that same color of blue for your backsplash.)
You can also use a stone for a rustic look or a subway tile, depending on the other elements in your kitchen.