You flush everything down the toilet, in small amounts at a time, after cutting it up in smaller bits. You don't put a big pile in and then flush, you flush and then gradually pour the stuff in as it's flushing so it doesn't plug up. Good to let leaf dry a bit first to reduce the bulk. If you freeze them in a plastic bag you can just crush them up by squeezing the bag instead of cutting them up. Stalks require cutting though, into sections about 1" long, then you flush them too. If it's fat stems you have to split them into small enough parts to be able to cut.
Taking weed waste anywhere outside the home is risky and therefore foolhardy, if not in a state that Obama ordered the DEA not to do their job in. If you really want to make sure you don't plug the drain you can grind the shit up into a smoothy and pour it down that way, at least the leaf.