What’s the best way to save jwt tokens in flutter apps?

You probably don’t want to store sensitive data in shared preferences. Instead you might want to look into a plugin like this:
https://pub.dartlang.org/packages/flutter_secure_storage

import 'package:flutter_secure_storage/flutter_secure_storage.dart';

// Create storage
final storage = new FlutterSecureStorage();

// Write value 
await storage.write(key: 'jwt', value: token);