While there is not a way to export an org chart through the UI, there are a couple of options available to you if you are interested in this type of feature.
1. If you would like to see this as an option available in a future release I would recommend submitting an idea to the Ideas for Jive space, where our Product team reviews through top rated ideas when considering features for future releases.
2. You can also leverage the API endpoints to build out a custom report/view of your org chart, for this you might find the Developer space helpful - Re: Is there a simple way to retrieve full org chart information for the company?