I must be confused about what the word "share" means. If you share a file with me, it is presumably with the intention that I am able to save a local copy and do something useful with it - some sort of data analysis, document corrections, or whatever. At the point you pass it to me, you lose any and all possibility of controlling what I actually do with it. Slack is irrelevant, there are plenty of ways for me to send it to other people. No amount of rights management can help with this, because the file needs to be unrestricted in order for it to be of any use to me.
Even if by "content" you mean useless crap like Powerpoint presentations, which could potentially be presented in-browser only and not allowed to download, you still face the same problem film companies keep running into. If I am able to view something on my monitor, I am able to make an unrestricted local copy of it, and there's nothing you can ever do to prevent it. At the very worst, that might mean taking photos of the screen, more likely just things like screenshots or finding temporary files. If I can see it, I can copy it.
So really the whole thing is nonsense. The complaint in this case seems to be essentially that if you send and email, the recipient can forward it someone else, which as Cronus notes is just stupid to complain about. But the more general issue is that the whole idea of being able to control files like that is stupid to start with. At the point you decide to send files to other people, you lose control over what happens to them afterwards. The problem is not with Slack or any other specific implementation of how to send them, it's that you're sending things to people you don't trust.