Between sheets of plastic wrap pound the thicker side of the breast to make it overall more even in thickness and season lightly with salt.
Heat the sesame oil in a skillet over moderate heat. Add the chicken breasts and tenderloins. Saute the chicken without disturbing the pieces for 4 to 5 minutes. You'll know to turn the chicken over when the top looks opaque (tenderloins may take only 2 to 3 minutes per side). Turn the chicken over to the other side and saute, undisturbed again for another 4 to 5 minutes or until the interior is cooked through.
Remove the chicken to a plate and discard the fat from the skillet. Squeeze the juice from the lime into the skillet and scrape up any coagulated juices into the juice; add the coconut milk, bring it to a simmer. Remove the skillet from the heat and whisk in the scallions and cilantro; season to taste with salt and dried red pepper flakes.