FlxTween can be used to change values over time following a number of available curve functions.

You can pass TweenOptions to any FlxTween, which can include an onStart and/or an onComplete callback.

Using these callbacks, you can trigger code to run when the tween starts, or when it completes.

// create a linear motion tween
FlxTween.linearMotion(myObject, fromX, fromY, toX, toY, duration, useDuration, {type: tweenType, easing: FlxEase: easeFunction, onStart: myStartCallback, onComplete: myCompleteCallback});

Demonstration

package;

import flixel.FlxG;
import flixel.FlxSprite;
import flixel.FlxState;
import flixel.tweens.FlxEase;
import flixel.tweens.FlxTween;

class PlayState extends FlxState
{
	var spriteA:FlxSprite;
	var spriteB:FlxSprite;
	
	override function create()
	{
		super.create();
		
		spriteA = new FlxSprite("assets/sprite.png");
		spriteA.x = spriteA.y = 50;
		add(spriteA);
		
		spriteB = new FlxSprite("assets/bigbox.png");
		spriteB.x = 50;
		spriteB.y = FlxG.height - spriteB.height - 50;
		add(spriteB);
		
		moveA();
	}
	
	private function moveA(?_):Void
	{
		FlxTween.linearMotion(spriteA, 50, 50, FlxG.width - spriteA.width - 50, 50, 1, true, {
			type: FlxTweenType.ONESHOT,
			ease: FlxEase.sineInOut,
			onComplete: moveB
		});
	}
	
	private function moveB(_):Void
	{
		FlxTween.linearMotion(spriteB, 50, FlxG.height - spriteB.height - 50, FlxG.width - spriteB.width - 50, FlxG.height - spriteB.height - 50, 1, true, {
			type: FlxTweenType.ONESHOT,
			ease: FlxEase.sineInOut,
			onComplete: moveABack
		});
	}
	
	private function moveABack(_):Void
	{
		FlxTween.linearMotion(spriteA, FlxG.width - spriteA.width - 50, 50, 50, 50, 1, true, {
			type: FlxTweenType.ONESHOT,
			ease: FlxEase.sineInOut,
			onComplete: moveBBack
		});
	}
	
	private function moveBBack(_):Void
	{
		FlxTween.linearMotion(spriteB, FlxG.width - spriteB.width - 50, FlxG.height - spriteB.height - 50, 50, FlxG.height - spriteB.height - 50, 1, true, {
			type: FlxTweenType.ONESHOT,
			ease: FlxEase.sineInOut,
			onComplete: moveA
		});
	}
}