You could chew some gum while intermittent fasting but since the gum contains some calories and sugar it could break the intermittent fasting so it's not recommended to chew gum.
If you chew gum while intermittent fasting you should use sugarless gum instead.
Chewing the gum may also trigger hunger and may cause you to crave some food so it could mess up the intermittent fasting so I would avoid any gum until the intermittent fasting is over with.
However when you're fasting you need to intake zero calories for the fasting to be effective so avoid anything with calories if possible.