Prior to November 30, 2015 you can access the Chart data by selecting the Chart in your Illustrator document, and clicking on the Edit in Creative Cloud button. Once in the Creative Cloud Charts service in the browser, go to the Data tab. You can copy the data from here to a spreadsheet which you can save to your desktop.
After November 30, 2015 you can go to assets.adobe.com, log in to your Creative Cloud account. Select Libraries from the menu on the left, and then select Charts. From here you can navigate to the charts that you’ve created using Creative Cloud Charts.