Preheat the oven to 375° F and line a couple of baking sheets with parchment paper.
Stir the flour, cream of tartar, baking soda and salt together in a medium bowl.
In a large mixing bowl, beat the coconut oil and sugar together with an electric mixer on high speed until creamy, about 2 minutes. Beat in the vanilla and milk.
Add the flour mixture to the coconut oil mixture, about a third at a time, beating it in completely between each addition. You may need to stir in the last addition by hand, as the dough will be pretty thick at this point.
Stir the cinnamon and sugar for rolling together in a small bowl.
Roll the dough into balls of about 2 tablespoons each, then roll each in the cinnamon-sugar to coat. Place the balls on the baking sheets, with about 2 inches between them.
Bake for 10 minutes and transfer to a cooling rack to cool. Once the cookies are cool, remove them from the baking sheets and serve.