Fill a saucepan with lightly salted water and bring to a rolling boil; stir in vermicelli noodles and cook, uncovered, stirring occasionally, until the noodles are tender yet firm to the bite, 4 to 5 minutes. Drain.

Heat oil in a large pot over medium heat; add onions, garlic, ginger, and turmeric. Cook and stir until onions start to brown, about 5 minutes. Stir in chicken, fish sauce, chile powder, and salt. Add a tablespoon or two of water if mixture looks dry or starts to stick. Cook until chicken is tender and no longer pink, about 5 minutes.

Pour milk and coconut milk into the pot. Bring the soup to a boil; reduce heat, and simmer, uncovered, stirring frequently, about 5 minutes.

Combine 1/2 cup water and chickpea flour in a small bowl. Add chickpea flour mixture to the soup a few tablespoons at a time; stir thoroughly between each addition to avoid lumps. Simmer until slightly thickened, 5 to 10 minutes.

Place cooled vermicelli noodles into servings bowls. Ladle soup over the noodles, and garnish with green onions and cilantro.