As you already know, that it is not good to chew gum if you are wearing braces. But still you like it. I am not sure , but before chewing gum you can lubricate you braces with some oil using your fingers or dipping a soft brush into the oil. This will prevent the gum from sticking to your braces.
Note of Caution : Try this with the oil that can be taken directly. Like olive oil(please confirm).