Preheat the oven to 350°F. (or 325°F. if using a dark or nonstick pan). Spray the bottom and sides of a 13x9-inch pan with baking spray with flour.
In a large bowl, beat the cake mix, 1/4 cup chai latte mix, the water, oil, and eggs with an electric mixer on low speed for 30 seconds. Beat on medium speed for 2 minutes, scraping the bowl occasionally. Stir in the chocolate chips. Pour into the prepared pan.
Bake for 29 to 40 minutes or until the center of the cake springs back when lightly touched. Cool completely, about 1 hour.
In a medium bowl, mix the confectioners' sugar and butter until smooth; set aside. In a microwavable bowl, microwave the milk on HIGH for 10 to 15 seconds until very warm. Stir in 1 T. dry chai latte mix until dissolved; stir into the confectioners' sugar mixture until smooth and spreadable. Spread over the cake. Just before serving, dust with cinnamon.