This is the biggest issue I have with Slack. Often I'll have like 5 different conversations involving different people all around the same thing, and the only way to bring them all together is to start a channel which then either sits around forever or eventually gets archived and disappears. There's no way to move messages from one channel to the other to collect a history of comments, so it's not terribly useful for advancing a concern from one group to another as it collects receipts. Instead, the old thread with the old receipt dies completely and the context has to be rebuilt for every new group of people you are talking to.
I hate DMs in Slack for this and many reasons. One thing I do try is to ask people to move to a public channel unless it's a personal issue. Copy/paste their question and cc their handle.