No having your teeth professionally whitened by a dentist is usually considered cosmetic and not a medical necessity so since it's only cosmetic the HSA and FSA will not cover the cost of the teeth whitening.
If you want to have your teeth professionally whitened you'll usually need to pay for the teeth whitening out of your own pocket.
You might have to get a personal loan or find a dentist that may have to give you a payment plan but teeth whitening is usually not covered by any health insurance or HSA or FSA.
Anything cosmetic for procedures are usually not covered by health insurance or dental insurance or HSA or FSA.
You'll have to pay out of pocket for the teeth whitening.