Probably not directly. I'm not sure what you mean by "task workflow storyboard", but most of the visuals in JIRA don't really export. It lets you have all the raw data you need, but not really the diagrams (not that it's stopping you, it's just "oh go look at it in JIRA, with current real live data" is usually more useful than "here's a diagram that's out of date because I saved it last week")
Maybe you could explain what you're trying to get out, and we can have a look?
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