To make the cake: Preheat oven to 350 degrees F. Grease two round cake pans, and line with parchment paper.
Sift together the flour, sugar, cocoa, baking soda and salt. Add the oil, vanilla, vinegar and water. Mix together using a hand mixer until smooth. Add chocolate chips.
Pour into pans and bake at 350 degrees for 35-45 minutes. Remove from oven and allow to cool for about one hour before removing from pans. Cool completely before frosting.
To make the frosting: Using a hand or stand mixer, mix together all ingredients until smooth and creamy, adding more or less non-dairy milk to achieve the desired thickness.