Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch cake pan.

Mix cake mix, flour, sugar, chai latte powder, and salt together in a large bowl using a fork. Set aside.

Combine sour cream, melted butter, eggs, heavy cream, and vanilla extract together in a bowl using an electric mixer. Add flour mixture and mix on medium speed for 1 minute; scrape down sides of bowl and mix about 1 minute more. Pour into the prepared pan.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 35 to 40 minutes.

Beat butter in a bowl using an electric mixer until fluffy. Slowly add confectioners' sugar, coffee creamer, and vanilla extract. Mix well. Add cinnamon and chai latte powder and mix using low speed until frosting is smooth.

Allow cake to cool completely, about 1 hour, before frosting.