How can we automatically export order reports?

You can get order reports from the “Reports” link at the top of Seller central.

If you’re looking for something that does this for you on a daily/weekly/monthly basis, there may be 3rd party softwares out there that can do it.
I know there is software available for feedback which you can give access to your account and it requests feedback reports regularly so IT can alert you when you get a bad feedback.

The same is likely possible with order reports.