Flutter checkbox unwanted touch space

Use SizedBox
The widget is basically made for resizing its child.

SizedBox(
    width: 15,
    height: 15,
    child: Checkbox(value: false, onChanged: null)
)

Try this then,

import 'package:flutter/material.dart';

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      title: 'NonStopIO',
      theme: new ThemeData(
        primarySwatch: Colors.red,
      ),
      home: new MyHomePage(),
    );
  }
}

class MyHomePage extends StatefulWidget {
  @override
  _MyHomePageState createState() => new _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  bool _rememberMeFlag = false;

  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(
        title: new Text('NonStopIO'),
      ),
      body: new Container(
        color: Colors.black38,
        child: new Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            new Container(
              margin: new EdgeInsets.symmetric(vertical: 5.0, horizontal: 35.0),
              color: Colors.white70,
              height: 50.0,
            ),
            new Container(
              margin: new EdgeInsets.symmetric(vertical: 5.0, horizontal: 35.0),
              color: Colors.white70,
              height: 50.0,
            ),
            new Container(
                margin: new EdgeInsets.symmetric(vertical: 5.0, horizontal: 20.0),
                child: new Row(
                  mainAxisAlignment: MainAxisAlignment.spaceBetween,
                  children: <Widget>[
                    new Row(
                      children: <Widget>[
                        new GestureDetector(
                          child: new Row(
                            children: <Widget>[
                              new Checkbox(
                                value: _rememberMeFlag,
                                onChanged: (value) => setState(() {
                                      _rememberMeFlag = !_rememberMeFlag;
                                    }),
                              ),
                              new Text(
                                "Remember me",
                                style: new TextStyle(color: Colors.white70),
                              )
                            ],
                          ),
                          onTap: () => setState(() {
                                _rememberMeFlag = !_rememberMeFlag;
                              }),
                        ),
                      ],
                    ),
                    new Container(
                      margin: new EdgeInsets.only(right: 15.0),
                      child: new Text(
                        "Forgot password ?",
                        style: new TextStyle(color: Colors.white70),
                      ),
                    )
                  ],
                )),
            new Container(
              margin: new EdgeInsets.symmetric(vertical: 5.0, horizontal: 35.0),
              color: Colors.orange,
              height: 50.0,
            ),
          ],
        ),
      ), // This trailing comma makes auto-formatting nicer for build methods.
    );
  }
}

Here, I have adjusted the margin to align the Checkbox and Forgot password Text.

You can achieve this by customising the Checkbox widget.

1. Create a CustomCheckbox using the exact code from flutter/packages/flutter/lib/src/material/checkbox.dart.

2. Add a new field to your CustomCheckbox widget

        final bool useTapTarget;
   

3. Make sure to add the new field to your constructor with it default value set to true.

        this.useTapTarget = true
   

4. Modify the build method in the _CheckboxState method. Add this block of code above the return call.

        Size noTapTargetSize = Size(CustomCheckbox.width, 
        CustomCheckbox.width);
        final BoxConstraints additionalConstraints = 
        BoxConstraints.tight(widget
           .useTapTarget? size : noTapTargetSize);
   

5. Finally, use your CustomCheckbox widget in your code, and set your custom field to false to remove material padding. example

   Container(
           margin: EdgeInsets.only(right: 15),
           child:CustomCheckbox(
               value: _checked,
               materialTapTargetSize: null,
               onChanged: _onCheckBoxChange,
               useTapTarget: false,
               activeColor: Colors.teal),
         )