List of Jira tickets that you can view and select which you're going to point. A jira ticket would be "selected" to be voted on which would then update each person's screen. Each person connected to the room would see the Jira issue number which would be clickable to open the story.
Once there's a vote on points there's an easy option to just say "update Jira".
The list of Jira stories could just pull from saved filters in Jira.