Whisk together coconut milk and sugar in a small saucepan. Bring to a boil over medium-high. Reduce heat to medium-low, and cook, whisking constantly, until sugar dissolves, about 10 minutes. Remove from heat, and cool almost completely, about 30 minutes. Chill 1 hour.
Process flaked coconut, lime juice, salt, 3 cups of the mango cubes, and 1 cup of the coconut syrup in a blender until smooth, about 20 seconds. (Store remaining coconut syrup in an airtight container in refrigerator up to 3 days.) Finely chop remaining 1 cup mango cubes; fold into mixture in blender.
Pour mixture evenly into 10 (2-ounce) plastic ice pop molds. Freeze 1 hour. Insert pop sticks, and freeze until solid, about 3 more hours.