What is the likelihood that a benign lesion caused from chronically biting or sucking the cheek will turn into cancer?

Highly unlikely. Highly unlikely. Higher risk factors for intraoral carcinomas and head/neck cancers include tobacco products, alcohol abuse, and hpv virus. See your primary care doctor for more details.
Traumatic fibroma. Repeated trauma to the buccal mucosa can result in a reactive change that results in a soft dome shaped tissue mass the same color as the surrounding mucosa. This is known as an irritation fibroma. Treatment is surgical excision. These are benign lesions, but cancers can occur in the mouth from viruses, smoking etc. So have it checked it by an ent/dentist.