At the moment Zinc does not support deleting a conversation. This feature is our on near term roadmap and we plan to release it in the upcoming months. In the meantime, there are several ways to remove messages from the app.
1. You can archive a conversation to remove it from your recents. When the conversation picks up again, you will be able to revisit it.
2. 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.
3. Have your Administrator set your "Zinc Clear" settings so that messages will auto-delete after a specific time frame.