To make blue syrup: Into a bowl, add Kool-Aid powder and water, and mix to combine. Whisk in the melted white chocolate until completely incorporated. If it sets or is a little too thick, you can add 1 drop of water at a time until you have a pourable consistency.
To make Frappuccino: Into a blender, add your ice, milk, vanilla ice cream, mango syrup, pink lemonade Kool-Aid powder, citric acid, and grenadine. Blend until smooth. If the color isn't vibrant enough, you can add more grenadine 1/4 teaspoon at a time.
To assemble: Pour the pink mango Frappuccino into the cup, filling it a third of the way full. Then drizzle the blue syrup around the inside of the cup, letting it drip down slightly. Top with remaining Frappuccino and whipped cream, and then sprinkle with pearl dust. Serve immediately.