I just did a deep dive into our app store, and I wasn't able to find any apps that directly integrate Shopify to Simply Accounting. One may have to be custom built, or you may have to use your Orders CSV to manually feed your accounting information into the app.
You may want to look into QuickBooks as an alternative that integrates well with Shopify. We actually provide an integration solution if you're interested. The integration is very clean between Shopify and QuickBooks.
If you download your shopify transactions using this app:
You can easily import them into Simply Accounting (it puts your income and expenses in a simple bank deposit/withdrawal format and combines a few shopify reports to do it). It will really work with any accounting software.
You may have already found a solution, however if not, please feel free to contact us at eBridge Connections. Our integration platform can connect Simply Accounting or Sage 50 Canadian with Shopify and enable automated, bi-directional data exchange between the two systems. Currently, we can integrate orders out of Shopify, and Shipment, Inventory, and Product Updates in from Simply Accounting.
You can build your own Simply Accounting-Shopify integration blueprint on our site at: http://www.ebridgeconnections.com/blueprint/