:D
So I tested this on Showdown (with you actually :P), and I had my Tyranitar Fling a Life Orb. When T-tar flung the Life Orb he did not lose any HP, so he didn't gain any boost from it, meaning he flung the Lfe Orb before it could boost Fling's power. Since the same boosting mechanics apply to Chice Band as they do to Life Orb, I think we can safely say that Fling does not get boosted by Choice Band