Is it possible to get stomach ulcers from chewing gum?

No. It is usually not possible to get stomach ulcers from chewing gum. Many stomach ulcers have been shown to be caused by a bacterial infection.
Not really. In theory at least this can be bad, as excess acid secretion in combination with pockets of damage to the stomach lining may lead to an ulcer. N fact as long as the gum is sugar free (and particularly if it contains xylitol) it is actually good for the teeth and can prevent dental cavities. However some moderation is necessary whichever type of gum he is eating. I'd suggest you limit him to thre.