Dice the mango and toss with the sugar in a small bowl. Let sit for about 30 minutes, stirring occasionally, until the fruit releases its juices and becomes glossy and syrupy.
Whisk together the coconut milk, maple syrup, lime zest and juice, and salt in a medium bowl. If the mixture doesn't smooth out by whisking, use a blender to force it into submission.
Gently fold in half of the macerated mango, along with any syrupy juices.
Divide the mixture evenly among the wells of two standard ice cube trays. Freeze until solid, about 4 hours. Once solid, pop your cubes into a resealable bag to keep them free of flavors from their neighbors in your freezer.
Just before serving, toast the coconut flakes in a dry skillet over medium heat, shaking frequently, until golden at the edges and fragrant, 5–8 minutes. Set aside.
Add the frozen cubes to a food processor. Pulse until coarsely chopped, then process until smooth and creamy, stopping to scrape down the sides as needed. If the mixture struggles to smooth out, let it sit for a few minutes to soften slightly, then process again.
Scoop the ice cream into bowls and top with toasted coconut and the remaining half of your diced mango. Serve immediately.