In a food processor, puree the cucumbers until smooth. Add the avocados, curry paste, sugar, lime zest and chile. Process until blended. Add 3 1/2 cups of water, the coconut milk and lime juice and process until smooth. Transfer the soup to a large bowl and season with salt. Cover and refrigerate until chilled, 15 minutes.
Meanwhile, in a skillet, toast the coconut over low heat, stirring a few times, until lightly browned and crisp, 3 minutes. Let cool.
Ladle the soup into small bowls or cups, garnish with the toasted coconut flakes and cilantro sprigs and serve.