You can store it using sqflite,hive or shared preferences.Try to save it under flutter shared preferences. These are two methods that you can use.
Using shared preferences
1)First create a shared preference instance
SharedPreferences prefs = await SharedPreferences.getInstance();
Then save the relevant data type.here you need to put a object list so add the list and convert it to the String using jsonEncode.
Map<String,List<Item>> map={mylist.id: mylist.list};
prefs.setString("itemList", json.encode(map));
Then you can retrieve data like this
Map<String,List<Item>> map=json.decode(prefs.getString("itemList")).asMap();
2)Using Hive
First Create the hive databse.you can put any name here
var box = Hive.box('myBox');
Then add the object in to that database
var myList = myList()
..id = your id here
..list = add list here;
var name = box.add(myList);
You can get anywhere this data list.
print(box.getAt(0));