How can I display buttons side-by-side in Flutter?

Column is for items vertically arranged (hence a column), you are looking for Row. Just replace Column with Row, the rest of the code is fine. You can also use an Expanded if you want to fill all the available space.

        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            Text(
              "Rahul Srivastava",
            ),
            Text(
              "Varanasi, India",
            ),
            Row(
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                FlatButton(
                    onPressed: () {
                      var player = AudioCache();
                      player.play('abc.mp3');
                    },
                    child: Text('Play')),
                FlatButton(
                    onPressed: () {
                      var player = AudioCache();
                      player.play('abc.mp3');
                    },
                    child: Text('Pause')),
              ],
            )
          ],
        ),

Wrap(
            children: <Widget>[
              RaisedButton(
                ...
              ),
              RaisedButton(
                ...
              ),
              RaisedButton(
                ...
              ),
            ],
          ),

If you have a column with text in it, and you want two buttons below that text right next to eachother you can use ButtonTheme.bar

Below is some of Flutter's starting code with it. You could plug it in to the starter to see it in action:

Just paste this after the second new text (the one with $counter in it)

        new ButtonTheme.bar(
        child: new ButtonBar(
        alignment: MainAxisAlignment.center,
        children: <Widget>[
                new RaisedButton(
                  onPressed: _incrementCounter,
                  child: new Icon(Icons.add),
                  color: Colors.green,
                ),
                new RaisedButton(
                  onPressed: _decrementCounter,
                  child: new Icon(Icons.remove),
                  color: Colors.red,
                ),
                  ],
        ),
        ),