Hello @aymeric ,
the is no way to export them. Playback is possible in Dyntarace UI only. The recommended way is to put the link to the session replay directly in the Jira ticket. If you have the replay screen for the session opened, just copy the URL from the browser. The user clicking on the link needs permissions to access and replay the session.
The workaround is only to use a screen recording tool of your choice and record the session replay in Dynatrace UI.