I would like to be able to add a flow to a survey that would allow it go through and approval process and update a list within SharePoint. The only options that I'm finding for the Survey app now is to export to Excel.
Like Mike Mentioned, you can create a workflow with
Call Http Web Service action to call SharePoint
rest api for creating/updating new item in Survey list.
You can use sharepoint designer to add your workflow to your List. Detailed steps are here.
Here are the references for CRUD operation on List Item with Rest API.