Preheat oven to 325 degrees F.
Place 1/3 cup of the sugar in the bottom of the flan pan. When sugar begins to melt, stir gently with a wooden spoon until it dissolves completely. Continue to cook, watching very carefully, until it turns a light brownish color then remove from heat immediately. Do not allow it to darken further as it will turn hard and unusable!
Place the bottom of the double boiler on the stove with water.
In a large bowl beat the eggs with a whisk until they are foamy. Beat in the condensed milk, coconut milk and vanilla and 1/4 cup of the coconut.
Pour the egg mixture on top of the caramel in the flan pan. Place pan on top of the double boiler. Steam for about 55 minutes to 1 hour. Check after 45 minutes. The flan is done when a sharp knife inserted in the flan comes out clean.
Remove from the double boiler, set on a rack to cool. Place in refrigerator and allow to chill for at least 2 hours, 3 is better.
Remove and let cool slightly. Run a knife around the edge of the pan. Place a plate on top of the pan and invert the flan onto the plate. Cut and serve.