AnimatedDefaultTextStyle

bool _first = true;

double _fontSize = 60;
Color _color = Colors.blue;

@override
Widget build(BuildContext context) {
  return Column(
    mainAxisSize: MainAxisSize.min,
    children: <Widget>[
      Container(
        height: 120,
        child: AnimatedDefaultTextStyle(
          duration: const Duration(milliseconds: 300),
          style: TextStyle(
            fontSize: _fontSize,
            color: _color,
            fontWeight: FontWeight.bold,
          ),
          child: Text('Flutter'),
        ),
      ),
      FlatButton(
        onPressed: () {
          setState(() {
            _fontSize = _first ? 90 : 60;
            _color = _first ? Colors.blue : Colors.red;
            _first = !_first;
          });
        },
        child: Text(
          "CLICK ME!",
        ),
      )
    ],
  );
}