Chill a medium bowl and the beaters of an electric mixer.
Place 2 of the cut-up mangoes in a food processor bowl or blender container. Cover and process or blend until smooth. Measure 1 cup of the puree; set aside.
Combine the sugar and gelatin in a medium saucepan. Stir in the water. Cook and stir over low heat just until gelatin is dissolved. Remove from heat. Stir in the 1 cup mango puree. Cool a few minutes to room temperature.
Beat whipping cream and coconut extract in the chilled bowl with an electric mixer on low speed until soft peaks form (tips curl). By hand, fold mango mixture into whipped cream. Chill until mixture mounds when spooned.
Divide half of the mango mixture among six individual dessert dishes. Divide kiwi slices and remaining cut-up mango among the dishes. Top with remaining mango mixture and the toasted coconut. Cover and chill for at least 4 hours or up to 24 hours or until set. Sprinkle with additional large flakes of toasted coconut. Makes 6 servings.