At the moment Zinc does not support deleting a conversation. However there are several ways to remove messages from the app so you do not see it in your recent conversations.
You can archive a conversation to remove it from your recents. When the conversation picks up again, you will be able to revisit it.
If you are in a group message, you can remove all users from the group and then proceed to create a new group where the previous conversations will no longer be available.
Have your Administrator set your "Zinc Clear" settings so that messages will auto-delete after a specific time frame.