Your Slack channel can be used only to receive notificaton for new ticket and ticket replies, also your support agent can add replies from the Slack channel.
It can not be used to created new ticket or communication with customers.
Only Support Agents can add replies from the Slack, if you have added customers to the Slack channel then customers can only view the replies but they can not add new reply to the ticket through slack.
Here is how the flow of ticket works:
New ticket created in SupportCandy ticketing system
Now, you will get a notification and new thread in the Slack Channel
Support Agents can reply to the thread to add new replies to the ticket.
Customer can add the reply to this thread but those replies will not be added to the ticket, it remains only in Slack.