select a button and deselect button flutter

You can use a custom widget for this. I am modifying your current code.
Create a state variable to hold selected index and on tap, change the index inside setState. To show vertical line(selected yellow) you can use if conditional state if (verticalLine)

class _FyxState extends State<Fyx> {
  Widget buttonRow(String dateTime, bool verticalLine, int buttonNumber) {
    return InkWell(
        onTap: () {
          print('select-deSelect');
          setState(() {
            _selectedIndex = buttonNumber - 1;
          });
        },
        child: Container(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.spaceEvenly,
            // crossAxisAlignment: CrossAxisAlignment.center,
            children: [
              buttonNumber == 1 ? SizedBox(height: 10) : SizedBox(height: 0),
              Text(
                dateTime,
                textAlign: TextAlign.center,
                maxLines: 2,
                style: TextStyle(
                  color: Color(0xFFCC306F),
                  fontSize: 13,
                  fontFamily: 'PingFang SC',
                  fontWeight: FontWeight.w400,
                  height: 1.38,
                  letterSpacing: -0.09,
                ),
              ),
              buttonNumber == 1 ? SizedBox(height: 15) : SizedBox(height: 10),
              if (verticalLine)
                Container(
                  width: 63,
                  height: 3,
                  decoration: BoxDecoration(color: Color(0xFFF2C547)),
                )
            ],
          ),
        ));
  }

  int _selectedIndex = 0;
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Column(
        children: [
          Row(
            children: [
              Expanded(flex: 1, child: buttonRow('直播中', _selectedIndex == 0, 1)),
              Container(color: Colors.black45, height: 50, width: 2),
              Expanded(flex: 1, child: buttonRow("今天n11月24日", _selectedIndex == 1, 2)),
              Container(color: Colors.black45, height: 50, width: 2),
              Expanded(flex: 1, child: buttonRow("星期一n11月25日", _selectedIndex == 2, 3)),
              Container(color: Colors.black45, height: 50, width: 2),
              Expanded(flex: 1, child: buttonRow("星期二n11月26日", _selectedIndex == 3, 4)),
            ],
          ),
        ],
      ),
    );
  }
}