This is a complete cluster --- if I've ever seen one! Screw the kick out flashing. You can't even see the baby tins for the shingles against the roof to wall. Probably no head or sill flashings. Tell the contractor to strip it off because he's an idiot. You need a rain screen. Not too fancy. Strip out the exterior with furring and then install a substrate which you glue the stone. He can vent the rain screen through a simple flashing detail up in the gables. Better yet, tell you client to walk and take the money. We will learn how to extract the project's precious metals from the landfill in the future anyway. It's great for repair guys like me to find this work , but, come on!