效果如下图：

代码

import 'package:flutter/material.dart';
import 'package:sprintf/sprintf.dart';  //这个是一个拼接字符串的flutter库，主要是为了使用方便，你可以选择不使用，这样的话你需要自己拼接图片路径

class ImagesAnimation extends StatefulWidget {

  final double w;
  final double h;
  final ImagesAnimationEntry entry;
  final int durationSeconds;

  ImagesAnimation({Key key, this.w : 80, this.h : 80, this.entry, this.durationSeconds : 3}):super(key:key);


  @override
  _InState createState() {
    return _InState();
  }
}

class _InState extends State<ImagesAnimation> with TickerProviderStateMixin{

  AnimationController _controller;
  Animation<int> _animation;

  @override
  void initState() {
    super.initState();
    _controller = new AnimationController(vsync: this, duration: Duration(seconds: widget.durationSeconds))
      ..repeat();
    _animation = new IntTween(begin: widget.entry.lowIndex, end: widget.entry.highIndex).animate(_controller);
//widget.entry.lowIndex 表示从第几下标开始，如0；widget.entry.highIndex表示最大下标：如7
  }

  @override
  Widget build(BuildContext context) {
    return new AnimatedBuilder(
      animation: _animation,
      builder: (BuildContext context, Widget child) {
        String frame = _animation.value.toString();
        return new Image.asset(
          sprintf(widget.entry.basePath, [frame]), //根据传进来的参数拼接路径
          gaplessPlayback: true, //避免图片闪烁
          width: widget.w,
          height: widget.h,
        );
      },
    );
  }

}

class ImagesAnimationEntry {
  int lowIndex = 0;
  int highIndex = 0;
  String basePath;

  ImagesAnimationEntry(this.lowIndex, this.highIndex, this.basePath);
}

使用的地方：

ImagesAnimation(w: 100, h: 100, entry: ImagesAnimationEntry(1, 7, "images/men_sport_%s.png")),
//"images/men_sport_%s.png" 表示图片在你本地的路径，%s会被下标代替