Contrary to Android, Apple does not provide API to get compatible applications. You will need to make the implementation to show the available apps and launch them yourself. Personally I've already done something similar to open other map applications than Apple Plans so it should definitely be possible.
You can check if a specific application is available by using the package url_launcher and its method canLaunch
by trying to launch the URL scheme of an application. For example Google Drive has the URL scheme googledrive://
so if I want to check for Google Drive's availability I will need to do as follow:
import 'package:url_launcher/url_launcher.dart';
bool isAvailable = await canLaunch('googledrive://');
And then I can open it by using the same URL scheme with the needed parameters:
import 'package:url_launcher/url_launcher.dart';
await launch('googledrive://docs.google.com/document/<my_document_url>');
But you will need to define yourself all the applications you are supporting in your application and you will have to create the choice modal dynamically in Flutter depending on the available apps.