How do you get rid of a chemical burn caused by tooth whitener?

Wash it. First step would be copious irrigation to remove the chemical. Following that, it really depends on the extent of burn, depth of burn, location, and how long ago it occurred. For a small burn which still has feeling, is pink, you could likely use neosporin or silvadene (silver sulfadiazine). Anything deeper, more extensive should be seen by doc.
Whitener burn. The burn will heal by itself over the next week to 10 days. You may be able to hasten the healing by applying vitamin E oil. You can get vitamin E capsules and squeeze the oil out onto the burn.