Do studies show bulimia as a significant risk factor for oral and esophageal cancers?

Maybe: There is increase risk for esophageal ulceration and that may lead to an increased risk for cancer , but no obvious link.

Not directly: The other issues associated with bulimia can increase the risk of developing esophageal cancer due to the increased irritation of thelining from the gastric acid and risk of perforation and trauma. Cancer of the esophagus can arise after prolonged irritation which causes mutations in the cells that line the inside. I am not aware of any specific studies in the oncology literature however there may be some in the behavioral sciences.