Almond milk should not cause any health issues, but it is not high on the recommended list of human foods that dogs can have. While almonds are not toxic to dogs, there are no known benefits to feeding almond milk to canines.
If you feel you need to share almond milk with your dog, be sure that you use plain almond milk without added sugars and flavors (never feed chocolate to dogs).
Whole almonds are not easily digested by dogs. They can cause stomach and gastric intestinal distress. Avoid any that have added salts and flavorings.
Most nuts are high in fat. This is another reason to avoid giving your dog almond milk.