This is a slightly modified version of the Tweens demo to showcase FlxTrail addon (original as3-version of this class was introduced at official flixel forum). Visit the original forum post for an alternative demo, which showcases how you can affect the trails behavior.
FlxTrail is a simple class that creates a group of duplicate sprites that follow some other sprite around. It's very simple to use, but make sure to read the comment above the constructor so you know what each parameter does.
Here's all of the code that added a trail to the main sprite in the Tweens demo://
sprite = new FlxSprite().loadGraphic(FlxAssets.imgLogo, true);
trail = new FlxTrail(sprite, FlxAssets.imgLogo, 25, 0, 0.4, 0.02);
sprite.offset.make(sprite.width * 0.5, sprite.height * 0.5);
add(trail);
add(sprite);
// Somewhere down the line, when you need to reset sprite's position:
trail.resetTrail();