Bring a large pot of salted water to a boil. Add 1 pound peeled and cleaned shrimp and remove from the heat. Cover and let sit until pink and cooked through, about 10 minutes.
Meanwhile, stir 1 (13 to 14-ounce) can of coconut milk until smooth, then add 3/4 teaspoon kosher salt and stir until combined (the dressing will taste salty, but it will be tempered by the other salad ingredients).
Transfer the shrimp with a slotted spoon to an ice water bath until cooled, then drain.
Bring the pot of water back to a boil, then add 20 ounces dried thin vermicelli noodles and cook according to package directions.
Meanwhile, dice 2 large mangoes (about 2 cups) and thinly slice 4 Thai chiles if using.
When the noodles are ready, drain, rinse with cold water, then drain again.
Divide the noodles among serving bowls, then pour the coconut dressing over the noodles. Top with the shrimp, mango, and Thai chiles or red pepper flakes.