Yes Dawn Dish Soap is great for killing fleas and flea eggs.
You can give your dog or cat a bath using Dawn Dish Soap and it will naturally kill the fleas without harming your dog, cat or other pet.
You can also wash clothing and bedding in Dawn dish soap to kill fleas or even put some Dawn Dish Soap in a bowl of water and put a light over it and the fleas will jump into the bowl of Dawn Dish Soap and the fleas will be killed and drown in the soap.