I have integrated Facebook functionality into my applications. By using the link https://github.com/facebook/facebook-ios-sdk, I have integrated the Facebook. In this application, at the time of login, it's opening Safari and at the same time the application is going to the background and then after login again it's coming back to the application. My intention is that this flow can accept the application store or not.
This is the official Facebook iOS SDK and many apps in App Store already use it. So you can use it inside your app.
Also, the flow in your question is exactly what the documentation of the library describes and is, again, used by apps that are already in App Store:
If the device is running in a version of iOS that supports multitasking, but it doesn't have the Facebook app of version 3.2.3 or greater installed, the SDK will open the authorization dialog in Safari. After the user grants or revokes the authorization, Safari redirects back to the calling app. Similar to the Facebook app based authorization, this allows multiple apps to share the same Facebook user access_token through the Safari cookie.
So, yes, there is nothing wrong with this flow.