Yes swishing coconut oil in your mouth can help to whiten teeth and keep teeth white.
I swish with coconut oil 4 times per week to keep my teeth white and it really does work.
I also do oil pulling with coconut oil where you swish the coconut oil around and then pull the coconut oil through your teeth.
The oil pulling not only helps to keep teeth white the oil pulling also removes bacteria and prevents tooth decay, cavities and even gum disease.
Be sure to brush your teeth right after oil pulling to remove the coconut oil from your teeth.