How can I make a "show up" text animation in Flutter?

You can compose widgets like this:

import 'dart:async';
import 'package:flutter/material.dart';

class ShowUp extends StatefulWidget {
  final Widget child;
  final int delay;

  ShowUp({@required this.child, this.delay});

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

class _ShowUpState extends State<ShowUp> with TickerProviderStateMixin {
  AnimationController _animController;
  Animation<Offset> _animOffset;

  @override
  void initState() {
    super.initState();

    _animController =
        AnimationController(vsync: this, duration: Duration(milliseconds: 500));
    final curve =
        CurvedAnimation(curve: Curves.decelerate, parent: _animController);
    _animOffset =
        Tween<Offset>(begin: const Offset(0.0, 0.35), end: Offset.zero)
            .animate(curve);

    if (widget.delay == null) {
      _animController.forward();
    } else {
      Timer(Duration(milliseconds: widget.delay), () {
        _animController.forward();
      });
    }
  }

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

  @override
  Widget build(BuildContext context) {
    return FadeTransition(
      child: SlideTransition(
        position: _animOffset,
        child: widget.child,
      ),
      opacity: _animController,
    );
  }
}

Then you can use it like this:

int delayAmount = 500;
...........
...........
...........
Column(
        children: <Widget>[
            ShowUp(
              child: Text("The first texto to be shown"),
              delay: delayAmount,
            ),

            ShowUp(
              child: Text("The text below the first"),
              delay: delayAmount + 200,
            ),

            ShowUp(
              child: Column(
                children: <Widget>[
                  Text("Texts together 1"),
                  Text("Texts together 2"),
                  Text("Texts together 3"),
                ],
              ),
              delay: delayAmount + 400,
            ),
          ],
        ),

Note that this "ShowUp" widgets can animate anything, not just texts.

I built a package to do this simply. delayed_widget

Example:
     DelayedWidget(            
            delayDuration: Duration(milliseconds: 200),// Not required
            animationDuration: Duration(seconds: 1),// Not required
              animation: DelayedAnimations.SLIDE_FROM_BOTTOM,// Not required
              child: Container(
                width: 200,
            height: 200,
            color: Colors.red,
          ))

There's an existing package called show_up_animation for it which is based on the implementation below.

This is a generalized widget to provide this animation. All you have to do is to wrap your widget(yes, any widget) inside SlideFadeTransition widget and voila!

It gives a lot of control. For example, you can control the amount, speed, direction, delay and even the curve of the animation.

///Wrapper class to implement slide and fade animations at the same time to
///a given element. Wrap the widget that you wish to appear with slide-fade
///transition in this class.
import 'dart:async';

import 'package:flutter/material.dart';

enum Direction { vertical, horizontal }

class SlideFadeTransition extends StatefulWidget {
  ///The child on which to apply the given [SlideFadeTransition]
  final Widget child;

  ///The offset by which to slide and [child] into view from [Direction].
  ///Defaults to 0.2
  final double offset;

  ///The curve used to animate the [child] into view.
  ///Defaults to [Curves.easeIn]
  final Curve curve;

  ///The direction from which to animate the [child] into view. [Direction.horizontal]
  ///will make the child slide on x-axis by [offset] and [Direction.vertical] on y-axis.
  ///Defaults to [Direction.vertical]
  final Direction direction;

  ///The delay with which to animate the [child]. Takes in a [Duration] and
  /// defaults to 0.0 seconds
  final Duration delayStart;

  ///The total duration in which the animation completes. Defaults to 800 milliseconds
  final Duration animationDuration;

  SlideFadeTransition({
    @required this.child,
    this.offset = 0.2,
    this.curve = Curves.easeIn,
    this.direction = Direction.vertical,
    this.delayStart = const Duration(seconds: 0),
    this.animationDuration = const Duration(milliseconds: 800),
  });
  @override
  _SlideFadeTransitionState createState() => _SlideFadeTransitionState();
}

class _SlideFadeTransitionState extends State<SlideFadeTransition>
    with SingleTickerProviderStateMixin {
  Animation<Offset> _animationSlide;

  AnimationController _animationController;

  Animation<double> _animationFade;

  @override
  void initState() {
    super.initState();
    _animationController = AnimationController(
      vsync: this,
      duration: widget.animationDuration,
    );

    //configure the animation controller as per the direction
    if (widget.direction == Direction.vertical) {
      _animationSlide =
          Tween<Offset>(begin: Offset(0, widget.offset), end: Offset(0, 0))
              .animate(CurvedAnimation(
        curve: widget.curve,
        parent: _animationController,
      ));
    } else {
      _animationSlide =
          Tween<Offset>(begin: Offset(widget.offset, 0), end: Offset(0, 0))
              .animate(CurvedAnimation(
        curve: widget.curve,
        parent: _animationController,
      ));
    }

    _animationFade =
        Tween<double>(begin: -1.0, end: 1.0).animate(CurvedAnimation(
      curve: widget.curve,
      parent: _animationController,
    ));

    Timer(widget.delayStart, () {
      _animationController.forward();
    });
  }

  @override
  Widget build(BuildContext context) {
    return FadeTransition(
      opacity: _animationFade,
      child: SlideTransition(
        position: _animationSlide,
        child: widget.child,
      ),
    );
  }
}

To use it, you just have to wrap your text widget or any widget for that matter with SlideFadeTransition widget. Below is a complete working example.

import 'dart:async';

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Show up Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: MyHomePage(title: 'Show up Demo'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

  final String title;

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

class _MyHomePageState extends State<MyHomePage> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            SlideFadeTransition(
              child: Text(
                'You have pushed the button this many times:',
              ),
            ),
            SlideFadeTransition(
              delayStart: Duration(milliseconds: 800),
              child: Text(
                '0',
                style: Theme.of(context).textTheme.display1,
              ),
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: () {
          setState(() {});
        },
        tooltip: 'Animate',
        child: Icon(Icons.add),
      ),
    );
  }
}

///Wrapper class to implement slide and fade animations at the same time to
///a given element. Wrap the widget that you wish to appear with slide-fade
///transition in this class.

enum Direction { vertical, horizontal }

class SlideFadeTransition extends StatefulWidget {
  ///The child on which to apply the given [SlideFadeTransition]
  final Widget child;

  ///The offset by which to slide and [child] into view from [Direction].
  ///Defaults to 1.0
  final double offset;

  ///The curve used to animate the [child] into view.
  ///Defaults to [Curves.easeIn]
  final Curve curve;

  ///The direction from which to animate the [child] into view. [Direction.horizontal]
  ///will make the child slide on x-axis by [offset] and [Direction.vertical] on y-axis.
  ///Defaults to [Direction.vertical]
  final Direction direction;

  ///The delay with which to animate the [child]. Takes in a [Duration] and
  /// defaults to 0.0 seconds
  final Duration delayStart;

  ///The total duration in which the animation completes. Defaults to 800 milliseconds
  final Duration animationDuration;

  SlideFadeTransition({
    @required this.child,
    this.offset = 1.0,
    this.curve = Curves.easeIn,
    this.direction = Direction.vertical,
    this.delayStart = const Duration(seconds: 0),
    this.animationDuration = const Duration(milliseconds: 800),
  });
  @override
  _SlideFadeTransitionState createState() => _SlideFadeTransitionState();
}

class _SlideFadeTransitionState extends State<SlideFadeTransition>
    with SingleTickerProviderStateMixin {
  Animation<Offset> _animationSlide;

  AnimationController _animationController;

  Animation<double> _animationFade;

  @override
  void initState() {
    super.initState();
    _animationController = AnimationController(
      vsync: this,
      duration: widget.animationDuration,
    );

    //configure the animation controller as per the direction
    if (widget.direction == Direction.vertical) {
      _animationSlide =
          Tween<Offset>(begin: Offset(0, widget.offset), end: Offset(0, 0))
              .animate(CurvedAnimation(
        curve: widget.curve,
        parent: _animationController,
      ));
    } else {
      _animationSlide =
          Tween<Offset>(begin: Offset(widget.offset, 0), end: Offset(0, 0))
              .animate(CurvedAnimation(
        curve: widget.curve,
        parent: _animationController,
      ));
    }

    _animationFade =
        Tween<double>(begin: -1.0, end: 1.0).animate(CurvedAnimation(
      curve: widget.curve,
      parent: _animationController,
    ));

    Timer(widget.delayStart, () {
      _animationController.forward();
    });
  }

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

  @override
  Widget build(BuildContext context) {
    return FadeTransition(
      opacity: _animationFade,
      child: SlideTransition(
        position: _animationSlide,
        child: widget.child,
      ),
    );
  }
}