Bots within Slack act just like users. You invite them to channels with /invite @nextup-jira or just @nextup-jira and then inviting the bot user to the channel.
Here are the docs from Slack - Invite members to a channel
Public / Private Channels
The bot will look for ticket numbers in your chats and provide you with quick issue summaries when you mention ticket numbers. You also got a link to the ticket, the status and the ticket title.
Chat Directly with the Bot
Start a chat with the bot just like any other user. When you provide ticket numbers in the private chat the bot responds with more details.