I would guess that actually anything you produced on company Slack is intellectual product that was produced during course of employment and as thus owned by the company. So no you can't ask it to be deleted.

EDIT: Now that I think more of it. This leads to somewhat interesting question about secrecy of correspondence. That is are the private messages protected? But on other hand would information posted on public or invite only channels be owned by company?

Probably depends on jurisdiction even inside EU.