There are various replies to this question, with each person talking out ones own experiences. Many are of the opinion that brushing before whitening makes sense as it helps to scrub off and make the teeth more even for the whitening strips or whitener to be applied. It may be all right to brush after whitening but it should be done gently.
Some contend that the whitening product used, as the product used for bleaching could involve the opening of the pores on the teeth and make them sensitive, with brushing with fluoride toothpaste helping to close them. It also pays to wipe off the excess bleach before it burns the gums. It is better to follow the dentists instructions like brushing and flossing the teeth before and after whitening treatment for good results.
To conclude as a general rule it is best to brush and floss before to remove bacteria and after the trays are removed to remove excess gel or whitening agent.