There is a saying "butterflies in my stomach(belly)". It is usually used when you are deeply in love with somebody and anytime they look at you or talk to you, you could feel a little tickle in your stomach that moves around.
So the full sentence "you can be the butterflies I feel in my belly" could mean "You could be the person I fall deeply in love with". I haven't ever heard the sentence said like that before, but my answer would be what I assume they would be saying.
Hope this helps.