Gravity can be simulated by setting the y acceleration of a FlxObject. You can even use maxVelocity to set a ‘terminal velocity’.

// object will accelerate downwards by 400 pixels per second
object.acceleration.y = 400;
// object will not accelerate beyond 200 pixels per second
object.maxVelocity.y = 200;

Demonstration

package;

import flixel.FlxG;
import flixel.FlxSprite;
import flixel.FlxState;

class PlayState extends FlxState
{
	var sprite:FlxSprite;
	
	override function create()
	{
		super.create();
		
		sprite = new FlxSprite("assets/sprite.png");
		sprite.x = FlxG.width / 2 - sprite.width / 2;
		sprite.acceleration.y = 600;
		sprite.maxVelocity.y = 200;
		
		add(sprite);
	}
	
	override function update(elapsed:Float)
	{
		super.update(elapsed);
		
		if (sprite.velocity.y > 0 && sprite.y >= FlxG.height + 8)
		{
			sprite.y = FlxG.height + 8;
			sprite.acceleration.y = 0;
			sprite.velocity.y = -100;
		}
		else if (sprite.velocity.y < 0 && sprite.y <= 0)
		{
			sprite.y = 0;
			sprite.velocity.y = 0;
			sprite.acceleration.y = 800;
		}
	}
}