Grease a 12-cup bundt pan with softened butter.
Add the dulce de leche, swirling to cover the bottom of the bundt pan. Set aside.
Spoon the chocolate batter into the bundt pan on top of the dulce de leche, making sure to fill the pan evenly. Using an angled spatula, smoothen the top.
Carefully pour the flan mixture into the bundt pan over the chocolate batter.
Cover the bundt pan with aluminum foil, securing the edges.
Set the bundt pan on a roasting pan and place it inside the oven. Carefully pour about two inches of hot water into the roasting pan.
In a 350 F oven, bake the cake for about 60 minutes without opening the oven door to keep the steam from escaping. After 60 minutes, check for doneness by inserting a toothpick in the center of the cake. If it comes out with some soft chocolate cake crumbs, the cake is ready.
Take the cake out of the oven and let it cool completely on the roasting pan. To release the cake, gently shake the roasting pan from side to side to loosen the cake.
Invert a serving plate over the bundt pan and carefully turn it over. Gently lift the bundt pan from the plate, releasing the cake.
Serve the flan cake right away or refrigerate to completely chill.