You are able to delete your own messages within a chat or channel. Click the ellipses on your message and you can then use the drop down menu selection of Delete to remove your own message.
You cannot delete old chat threads, but you can hide them by clicking the ellipses and choosing Hide.Sara commented
The ability for the teacher (owner) of the team to delete old conversations and responses that are inappropriate
Unfortunately I need to switch this back to Under Review. The feature team is investigating how best this could be implemented.