Preheat the oven to 450 degrees F (230 degrees C). Grease and flour two 4-ounce ramekins, tapping out any excess flour.

Place dark chocolate, milk chocolate, almond paste, and butter in a microwave-safe bowl. Microwave on high for 20 seconds at a time until butter is melted and mixture is hot, 1 to 1 1/2 minutes. Set aside and allow chocolate to continue melting for 1 minute longer. Whisk mixture until smooth but slightly grainy from the almond paste.

Combine sugar, egg, and egg yolk in a small bowl; beat with an electric mixer until it becomes very light lemon yellow in color and has doubled or tripled in volume. Fold cooled melted chocolate mixture into egg and sugar mixture until well incorporated. Stir in flour. Divide batter evenly between the prepared ramekins and sprinkle coconut flakes on top.

Bake in the preheated oven until the sides are firm but centers are still soft, 7 to 8 minutes. Allow to rest for 1 minute, then carefully invert ramekins on dessert plates and dust with powdered sugar. Serve immediately.