How to execute a method after the execution of another method in Flutter(Dart)

You need to make your method Asynchronous

you can use futures, async, await

Try this way

Make your first method async method like below example

Future<int> methodOne() async {
    debugPrint('first method called');
    sleep(const Duration(seconds: 3));
    return 4;

  }
  methodTwo() {
    debugPrint('second method called');
  }

now you can call your methods like this

          GestureDetector(
              onTap: () async {
                await methodOne().then((value) {
                  methodTwo();
                });
              },
              child: Center(child: Padding(
                padding: const EdgeInsets.all(20.0),
                child: Text("Click Me"),
              ))), 

For more information please read Asynchronous programming in flutter