Yes you can eat salmon skin.
Salmon Skin is edible but just be aware that salmon skin may make some people sick because of the contaminants that could be present in the salmon skin that gets absorbed by the salmon when it's in the water.
However for most people they can safely eat salmon skin.
I always eat the skin of the salmon when I eat salmon and I've never gotten sick from it.
However I always fully cook my salmon and fully cook the salmon skin because when you cook the salmon and salmon skin the bacteria and other contaminates that could make you sick are killed off by the heat of the cooking of it.
You can also eat salmon raw but it's not recommended because bacteria could be present that could make you sick so it's best to cook the salmon all the way before eating it.