I am using Firestore as a database for my flutter app. Some actions on my app lead to change/update in Firestore data.
I am using Flutter native notifications which are generated once a button is clicked. However, the data passed to the notification remains constant despite the data having been updated later in the Firestore.
I would like to implement a feature similar to the one present in sport apps where the live score is updated regularly in the notification.
How can I achieve that in my app? Do I have to use Firestore Cloud Messaging? Citing resources would be helpful.
What you want to achieve sounds like an ideal case for Firebase Cloud Messaging to be used. I recommend that you take a look at the FlutterFire documentation for Cloud Messaging both overview and usage, which should give you a good starting point.
Alternatively you can also use a Cloud Function as the host of FCM and only configure your app to receive messages, you can watch this video for insights on how to create the Cloud Function side.