This unfortunately is not possible, because notifications are not stored anywhere. They exist in memory on the device, until the user dismisses them, or they are replaced with a message of a similar ID, or the OS just removes them altogether.
Your best bet, is to generate a table on your mobile backend, that will store these notifications (the same ones that will be broadcasted to the users notification center), then get the app to read directly from this table, and store it on a local SQLite database.
These notifications that are broadcasted, will need to be sent from the backend itself, with the exact same content, as that being stored on the table I mentioned. This will ensure data integrity between the notification center, and that of the app.
[EDIT]
Please make sure that you use FCM (Firebase Cloud Messaging) for mobile push notifications. These are completely free, as per the documentation:
https://firebase.google.com/docs/cloud-messaging
For Tutorials, please look at these:
https://medium.com/@jun.chenying/flutter-tutorial-part3-push-notification-with-firebase-cloud-messaging-fcm-2fbdd84d3a5e
https://www.freecodecamp.org/news/how-to-add-push-notifications-to-flutter-app/
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