Horizontal item selector inspired by this design https://dribbble.com/shots/6591397-Travel-Application/attachments.

item_selector.dart

import 'package:flutter/material.dart';

class ItemTextStyle {
  const ItemTextStyle({
    @required this.initialStyle,
    @required this.animatedStyle,
  });

  final TextStyle initialStyle;
  final TextStyle animatedStyle;
}

class ItemSelectorBar extends StatelessWidget {
  const ItemSelectorBar({
    Key key,
    @required this.activeIndex,
    @required this.onTap,
    @required this.items,
    this.animatedTextStyle = const ItemTextStyle(
        initialStyle: TextStyle(color: Colors.grey, fontSize: 14),
        animatedStyle: TextStyle(color: Colors.white, fontSize: 14)),
    this.itemPadding = const EdgeInsets.all(8.0),
  }) : super(key: key);

  final int activeIndex;
  final ValueChanged<int> onTap;
  final List<String> items;
  final EdgeInsetsGeometry itemPadding;
  final ItemTextStyle animatedTextStyle;

  @override
  Widget build(BuildContext context) {
    return Container(
      color: Theme.of(context).primaryColor,
      child: Row(
        mainAxisAlignment: MainAxisAlignment.spaceEvenly,
        children: [
          for (int index = 0; index < items.length; index++)
            Padding(
              padding: itemPadding,
              child: ItemSelector(
                index: index,
                name: items[index],
                activeIndex: activeIndex,
                style: animatedTextStyle,
                onTap: onTap,
              ),
            )
        ],
      ),
    );
  }
}

class ItemSelector extends StatefulWidget {
  const ItemSelector({
    Key key,
    this.name,
    this.index,
    this.activeIndex,
    this.style,
    this.onTap,
  }) : super(key: key);
  final String name;
  final int index;
  final int activeIndex;
  final ItemTextStyle style;
  final ValueChanged<int> onTap;

  @override
  _ItemSelectorState createState() => _ItemSelectorState();
}

class _ItemSelectorState extends State<ItemSelector> with SingleTickerProviderStateMixin {
  bool _isSelected;
  Animation<TextStyle> _textStyle;
  AnimationController _controller;
  @override
  void initState() {
    super.initState();
    _isSelected = widget.activeIndex == widget.index;
    _controller = AnimationController(
      vsync: this,
      duration: const Duration(milliseconds: 250),
      value: _isSelected ? 1.0 : 0.0,
    );

    _textStyle = TextStyleTween(begin: widget.style.initialStyle, end: widget.style.animatedStyle).animate(_controller);
  }

  @override
  void didUpdateWidget(ItemSelector oldWidget) {
    super.didUpdateWidget(oldWidget);
    _isSelected = widget.activeIndex == widget.index;
    animateSelected();
  }

  void animateSelected() {
    if (_isSelected) {
      _controller.forward();
    } else {
      _controller.reverse();
    }
  }

  @override
  void dispose() {
    super.dispose();
    _controller.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return GestureDetector(
      onTap: () => widget.onTap(widget.index),
      child: AnimatedBuilder(
        animation: _controller,
        builder: (context, _) {
          return Column(
            mainAxisSize: MainAxisSize.min,
            children: <Widget>[
              Text(
                widget.name,
                style: _textStyle.value,
              ),
              CustomPaint(
                painter: _CirclePainter(
                  radius: 4.0,
                  animation: _controller,
                  verticalSpacing: 10,
                  circleColor: Colors.redAccent,
                ),
              ),
            ],
          );
        },
      ),
    );
  }
}

class _CirclePainter extends CustomPainter {
  _CirclePainter({
    @required this.radius,
    @required this.animation,
    this.verticalSpacing = 5.0,
    this.strokeWidth = 10.0,
    this.circleColor = Colors.redAccent,
  }) : super(repaint: animation);
  final double radius;
  final Animation<double> animation;
  final double verticalSpacing;
  final double strokeWidth;
  final Color circleColor;

  @override
  void paint(Canvas canvas, Size size) {
    final Paint paint = Paint()
      ..color = circleColor
      ..strokeWidth = strokeWidth;
    canvas.drawCircle(
      Offset(size.width / 2, size.height / 2 + verticalSpacing),
      radius * animation.value,
      paint,
    );
  }

  @override
  bool shouldRepaint(_CirclePainter oldDelegate) => oldDelegate.animation != animation;
}