Heat the cooking oil in a pot. Saute the lemongrass, galangal, kaffir lime leaves and chilies. Drizzle with fish sauce. Continue sautéing until the vegetables are soft and aromatic.
Pour in the fish broth. Stir. Taste. Add more fish sauce, as needed. Bring to the boil.
Add the yard-long beans. Cover the pot, lower the heat and simmer until the beans are done.
Add the flaked fish.
Pour in the coconut milk. Heat just until simmering.
Turn off the heat. Pour in just enough kalamansi (or lime or lemon) juice to add tang but not overwhelm the natural sweetness of the coconut milk.
Serve the Thai fish coconut milk soup at once. Garnish with cilantro and lime or lemon wedges.