Jira does have a “Start Standup” button, but it’s hidden and not well documented.

To enter start a standup in Jira, open an active Kanban-style board.

If there’s a “Start Standup” button in the upper right (this appears to be experimental), click it.

Your board converts to a simplified standup presentation!

On the left, each team member is listed in random order, which you can shuffle. I like to mix up the order of reports every day, so this feature helps me do that. Teammates can also be skipped.

You can assign a timer for each member that restarts as you switch. The default is two minutes, which is great… get on with it!

When you’re finished, click the “End Standup” button.

I’ve seen some griping about this feature in the Atlassian forums. All I can say is that the version that’s been presented to me is fantastic!