Aren't you limited to just 1 attack/round with the sling because it normally takes a move action to reload? Seems a bow is still the better route...I would say do the honorable thing and play a halfling rogue who uses a sling to maximize your attack bonus and get your sneak attack for the damage portion.
EDIT: Hmm. I see it. Page 141 of Players Handbook. The problem with this is that a flask is in a weird space of being a weapon you draw and being a stored item. Apparently it comes down to context -- if the storage device lends itself to Quick Draw, then Quick Draw applies. If not, then it's a rummaging-in-the-pack retrieval issue. I guess in such a case, the only good option for a halfling thrower is to buy the bandolier. At least there is SOME option that works.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.