On every JIRA issue page you can find new "Slack" tab in the Activity section (near Comments). If the issue you are looking at has a dedicated channel assigned you will be able to quickly join the Slack discussion directly from JIRA.
After opening the "Slack" tab you will see up to 100 most recent messages on that channel.
Moreover you can join Slack conversation directly from here as the input field below the last message lets you send messages back to that channel.
Due to technical limitation messages sent by others will not appear immediately. Selecting an input field and typing inside this field is also likely to trigger refresh. At last you can manually request checking for new messages by clicking the small "Refresh now" link below the last message.