How to create radio button with image in Flutter

You can try this approach:

int _value = 0;

@override
Widget build(BuildContext context) {
  return Scaffold(
    appBar: AppBar(),
    body: Padding(
      padding: const EdgeInsets.all(20.0),
      child: Row(
        children: <Widget>[
          GestureDetector(
            onTap: () => setState(() => _value = 0),
            child: Container(
              height: 56,
              width: 56,
              color: _value == 0 ? Colors.grey : Colors.transparent,
              child: Icon(Icons.call),
            ),
          ),
          SizedBox(width: 4),
          GestureDetector(
            onTap: () => setState(() => _value = 1),
            child: Container(
              height: 56,
              width: 56,
              color: _value == 1 ? Colors.grey : Colors.transparent,
              child: Icon(Icons.message),
            ),
          ),
        ],
      ),
    ),
  );
}