How do I add menthol flavoring to this gum?
The recipe already tells you when to add the flavoring. The menthol gives it that minty kick ("cold" feeling) and is used in more than one bubblegum flavoring, like mint, peppermint, sometimes cherry. 

For industrial applications it is easier to buy powder and then compound it into the flavor, but for home applications I recommend that you buy a mint flavor solution instead of just straight up adding menthol, since a mint flavor is more than that.