ElevatedButton without elevation at all.

main.dart

import 'package:flutter/foundation.dart';
import 'package:flutter/material.dart';

/// Дефолтный класс [_ElevatedButtonDefaultElevation] добавляет к elevation различные значения в зависимости от состояния кнопки
@immutable
class ZeroElevationProperty extends MaterialStateProperty<double>
    with Diagnosticable {
  ZeroElevationProperty();

  @override
  double resolve(Set<MaterialState> states) => 0;
}

@immutable
class ElevatedButtonBackground extends MaterialStateProperty<Color>
    with Diagnosticable {
  ElevatedButtonBackground(this.primary, this.hovered);

  final Color primary;
  final Color hovered;

  @override
  Color resolve(Set<MaterialState> states) {
    if (states.contains(MaterialState.hovered)) return hovered;
    return primary;
  }
}

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      debugShowCheckedModeBanner: false,
      theme: ThemeData(
        primarySwatch: Colors.blue,
        elevatedButtonTheme: ElevatedButtonThemeData(
          style: ElevatedButton.styleFrom(
            elevation: 0,
            minimumSize: const Size(120, 48),
            shape: const RoundedRectangleBorder(
              borderRadius: BorderRadius.all(Radius.circular(6)),
            ),
          ),
        ),
      ),
      home: MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  final String title;
  MyHomePage({Key? key, required this.title}) : super(key: key);

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            ElevatedButton(onPressed: () {}, child: const Text('Default')),
            const SizedBox(height: 16),
            ElevatedButton(
                style: ElevatedButton.styleFrom().copyWith(
                  elevation: ZeroElevationProperty(),
                  backgroundColor: ElevatedButtonBackground(
                    Theme.of(context).accentColor,
                    Colors.red,
                  ),
                ),
                onPressed: () {},
                child: const Text('Zero elevation')),
          ],
        ),
      ),
    );
  }
}