I have set up stories as work elements to which Tasks are related representing portions of work required to complete the Story. The tasks are assigned duration times to complete. Can a burndown chart be run in Jira to indicate progress?
Yes, Jira Software has burndown charts.
When a story issue (with an estimate on it) goes into the last column of a scrum board, it is considered "done" and burndown happens then.
Note that your "linked tasks" are separate entities, your scrum board will need to include people moving those tasks to "done" as well.
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