Preheat the oven to 350°F.
Spread the coconut flakes onto a small baking sheet and bake, keeping a very close eye as it burns easily, until lightly golden, 2 to 3 minutes.
In a dry small skillet, toast the pistachios over medium-low heat, tossing frequently, until lightly golden and very fragrant, about 5 minutes. Immediately remove the nuts from the pan and transfer to a bowl to stop the cooking process.
In 4 clear, 2-cup coupe glasses or dessert goblets, stack the pineapple, mango, coconut, pistachios, and several of the balsamic-infused figs. Garnish with a light drizzle of the balsamic fig syrup and the mint leaves and the scoop the sorbet over the top.