Welcome to the Fusion 360 community! At this time it is not possible to export an SVG file. However, you can get another vector format, DXF. You can get to this option by right clicking on a Sketch and selecting Save as DXF.
I note that you can request feature enhancements for Fusion 360 in the Ideastation, link below.
http://forums.autodesk.com/t5/ideastation-request-a-feature-or/idb-p/125
I hope that helps! Let us know if you have any other questions.
Thanks,
I took a quick look and did not find any existing requests for exporting sketches to SVG files. I am not aware of any immediate plans to implement this feature at this time.
If you make a request in the Ideastation, the status of the Idea may provide some clue. You can learn more about the Ideastation status's in the below link.
http://www.autodesk.com/products/fusion-360/blog/ideastation-update/
If you post the link back here, I'll be happy to add a vote to the suggestion!
Thanks,