Preheat oven to 350°F (175°C). Grease a Bundt pan.
In a mixing bowl, combine gluten-free flour, cocoa powder, sugar, baking powder, baking soda, and salt.
Add melted butter, eggs, vanilla extract, and buttermilk. Mix until smooth.
Pour the cake batter into the prepared Bundt pan.
In a blender, combine sweetened condensed milk, evaporated milk, eggs, and vanilla extract. Blend until smooth.
Slowly pour the flan mixture over the cake batter in the Bundt pan.
Cover the Bundt pan with aluminum foil and place it in a larger baking dish. Fill the larger dish with hot water to create a water bath.
Bake for 60 minutes or until a toothpick inserted into the cake comes out clean.
Remove from the oven and let it cool in the pan for 15 minutes. Then, invert onto a serving plate and let it cool completely before serving.