Try this..
From the data panel, select Open Details in A360.
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This will open up the item details in the A360 Dashboard within your web browser. From the tools drop down menu, you can choose Export to access the DWG option in the Export dialog box.
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DWG Option:
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Select Export and the Autodesk Translation service (cloud based service) will translate your file into a new DWG file. This file will be placed in the Project specified in the Export dialog. In the case, screenshot above, the project is called "Nathan's Data (DO NOT SHARE)." To access the file, close the Item Details page and then browse to that Project's home page in the A360 Dashboard via the web browser. The below screenshot includes some tips that show what the home page of the Nathan's Data (DO NOT SHARE) project look like. You should be able to find the DWG file in the activity feed or the Recent list after the translation is complete.
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To download the file to your desktop, select the Download option form the Actions drop down menu.
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This will put a copy on your desktop.
Please keep in mind that if you are sharing this file with someone, you don't need to go through this process. All you need to do is share a public link with the person. The public link will allow the person downloading a Fusion 360 design to get the file in the format of their choice.
To see what it looks like on the users's end, below is a public link for the Chain Sample (Fusion 360 Design). You'll note that it will allow you to download the file in the format of your choice.
http://a360.co/1z0jBmx
You can read more about sharing a public link in the data exchange tip.
Let me know if this helps or if you have any questions.
Thanks,
Nathan Chandler
Principal Specialist