Try below code hope its help to you I have try it other way
Only Single Checkbox Selected:
Your List :
List _texts = [
{
"value": false,
"site": "google.com",
},
{
"value": false,
"site": "youtube.com",
},
{
"value": false,
"site": "yahoo.com",
},
{
"value": false,
"site": "gmail.com",
},
];
Your Widget:
Padding(
padding: const EdgeInsets.symmetric(horizontal: 24.0, vertical: 64.0),
child: Column(
children: List.generate(
_texts.length,
(index) => CheckboxListTile(
controlAffinity: ListTileControlAffinity.leading,
contentPadding: EdgeInsets.zero,
dense: true,
title: Text(
_texts[index]["site"],
style: const TextStyle(
fontSize: 16.0,
color: Colors.black,
),
),
value: _texts[index]["value"],
onChanged: (value) {
setState(() {
for (var element in _texts) {
element["value"] = false;
}
_texts[index]["value"] = value;
});
},
),
),
),
),
Full Code:
import 'package:flutter/material.dart';
void main() => runApp(MyApp());
class MyApp extends StatelessWidget {
@override
Widget build(BuildContext context) {
return MaterialApp(
home: Scaffold(
appBar: AppBar(
title: Text("Flutter Single Checkbox Example"),
),
body: SafeArea(
child: Center(
child: CheckboxWidget(),
))),
);
}
}
class CheckboxWidget extends StatefulWidget {
@override
CheckboxWidgetState createState() => new CheckboxWidgetState();
}
class CheckboxWidgetState extends State {
List _texts = [
{
"value": false,
"site": "google.com",
},
{
"value": false,
"site": "youtube.com",
},
{
"value": false,
"site": "yahoo.com",
},
{
"value": false,
"site": "gmail.com",
},
];
@override
Widget build(BuildContext context) {
return Padding(
padding: const EdgeInsets.symmetric(horizontal: 24.0, vertical: 64.0),
child: Column(
children: List.generate(
_texts.length,
(index) => CheckboxListTile(
controlAffinity: ListTileControlAffinity.leading,
contentPadding: EdgeInsets.zero,
dense: true,
title: Text(
_texts[index]["site"],
style: const TextStyle(
fontSize: 16.0,
color: Colors.black,
),
),
value: _texts[index]["value"],
onChanged: (value) {
setState(() {
for (var element in _texts) {
element["value"] = false;
}
_texts[index]["value"] = value;
});
},
),
),
),
);
}
}
Result Screen-> 
Multiple Checkbox Selection
Your List/Map
Map<String, bool> values = {
'google.com': false,
'youtube.com': false,
'yahoo.com': false,
'gmail.com': false,
};
Your Function:
var tmpArray = [];
getCheckboxItems() {
values.forEach((key, value) {
if (value == true) {
tmpArray.add(key);
}
});
print(tmpArray);
tmpArray.clear();
}
Your Widget:
Column(
children: <Widget>[
ListView(
shrinkWrap: true,
children: values.keys.map((String key) {
return new CheckboxListTile(
title: new Text(key),
value: values[key],
onChanged: (value) {
setState(() {
values[key] = value!;
});
},
);
}).toList(),
),
const SizedBox(
height: 100,
),
ElevatedButton(
child: Text(
" Checkbox Items ",
style: TextStyle(fontSize: 18),
),
onPressed: getCheckboxItems,
),
],
)
Full Example
import 'package:flutter/material.dart';
void main() => runApp(MyApp());
class MyApp extends StatelessWidget {
@override
Widget build(BuildContext context) {
return MaterialApp(
home: Scaffold(
appBar: AppBar(
title: Text("Flutter Multiple Checkbox Example"),
),
body: SafeArea(
child: Center(
child: CheckboxWidget(),
))),
);
}
}
class CheckboxWidget extends StatefulWidget {
@override
CheckboxWidgetState createState() => new CheckboxWidgetState();
}
class CheckboxWidgetState extends State {
Map<String, bool> values = {
'google.com': false,
'youtube.com': false,
'yahoo.com': false,
'gmail.com': false,
};
var tmpArray = [];
getCheckboxItems() {
values.forEach((key, value) {
if (value == true) {
tmpArray.add(key);
}
});
print(tmpArray);
tmpArray.clear();
}
@override
Widget build(BuildContext context) {
return Column(
children: <Widget>[
ListView(
shrinkWrap: true,
children: values.keys.map((String key) {
return new CheckboxListTile(
title: new Text(key),
value: values[key],
onChanged: (value) {
setState(() {
values[key] = value!;
});
},
);
}).toList(),
),
const SizedBox(
height: 100,
),
ElevatedButton(
child: Text(
" Checkbox Items ",
style: TextStyle(fontSize: 18),
),
onPressed: getCheckboxItems,
),
],
);
}
}
Result Screen-> 
Refer Video Tutorial for Flutter Multiselect Dropdown Checkbox on YouTube