In a large bowl combine the tamarind, warm water, fish sauce, soy sauce, red pepper flakes, ginger, lemongrass, and garlic. Stir well. Place the chicken into a large bowl or plastic bag. Pour the marinade over the chicken, cover and let marinate in the fridge for 6 to 24 hours. Turn the chicken every few hours to ensure the chicken is evenly immersed in the marinade.
When ready to cook, heat the oven to 375 degrees. Remove the chicken from the marinade, pat dry and set aside.
In a large braising dish heat the canola oil over medium-high heat for 3 to 4 minutes. Once hot, place the chicken, skin side down, and brown for 4 to 5 minutes. Reduce the heat to medium and flip the chicken over. Cook the other side for 2 minutes.
Remove the chicken from the braising dish and set aside. Add the marinade, coconut milk and lime juice into the braising pan. Stir to combine and to deglaze the pan. Bring the cooking liquid to a simmer. Add the chicken (and its remaining pan juices) back into the braising pan. Place into the oven and cook for 20 to 25 minutes or until the chicken reaches 165 degrees.
While the chicken braises, add the corn starch into a small bowl and set aside.
Once the chicken has cooked for 20 to 25 minutes, remove the pan from the oven and place onto the cooktop. Remove the chicken, place onto a serving platter, cover and set aside.
Warm the pan over medium-high heat and bring to a boil. Add a few spoonfuls of simmering liquid to the corn starch and whisk until all lumps are gone. Pour the slurry into the pan and simmer sauce for 5 to 10 minutes or until thickened. Stir occasionally to prevent burning.
Top the chicken with the pan sauce and fresh lime juice. Serve warm with cooked jasmine rice. Salt to taste.