Heat oil in a pot over medium high heat. Add garlic, shallot, ginger, chile, turmeric, and salt and cook, stirring often, until soft and fragrant, about 3-4 minutes.
Add the rice and cook, stirring often, until rice is well coated and shiny, about 1 minute. Add the chicken broth and the chicken breast. Bring to a boil, then reduce heat and cook, covered, until rice is tender and chicken is cooked through, about 12-15 min.
Remove chicken from pot, and shred using two forks. Return shredded chicken to the pot, along with the coconut milk, lime juice, and fish sauce. Season to taste with additional salt if needed.
Increase heat and bring soup just to a boil, then reduce heat to low once more and stir in the spinach until just wilted. Ladle into bowls and serve. Top with chile flakes for extra heat if desired.