There are many ways to implement a jumping mechanic, but the simplest method is to add negative y velocity temporarily to a FlxObject with positive y acceleration, using some kind of timer to limit the jump time.

FlxG.collide(box, sprite);

var jumpPressed:Bool = pad.buttonA.pressed;

if (jumping && !jumpPressed)
	jumping = false;

/*
 * Reset jumpTimer when touching the floor
 * Note: This sprite's touching flags are set via FlxG.collide,
 * and are reset to false on super.update
 */
if (sprite.isTouching(DOWN) && !jumping)
	jumpTimer = 0;

if (jumpTimer >= 0 && jumpPressed)
{
	jumping = true;
	jumpTimer += elapsed;
}
else
	jumpTimer = -1;

// hold button to jump higher (up to 0.25s)
if (jumpTimer > 0 && jumpTimer < 0.25)
	sprite.velocity.y = -300;

Demonstration

package;

import flixel.FlxG;
import flixel.FlxSprite;
import flixel.FlxState;
import flixel.ui.FlxVirtualPad;

class PlayState extends FlxState
{
	var sprite:FlxSprite;
	var box:FlxSprite;
	var pad:FlxVirtualPad;

	var jumpTimer:Float = 0;
	var jumping:Bool = false;

	override public function create()
	{
		bgColor = 0;

super.create();

		sprite = new FlxSprite("assets/sprite.png");
		sprite.x = FlxG.width / 2 - sprite.width / 2;
		sprite.acceleration.y = 900;
		sprite.maxVelocity.y = 300;
		add(sprite);

		box = new FlxSprite("assets/bigbox.png");
		box.x = FlxG.width / 2 - box.width / 2;
		box.y = FlxG.height * 0.75 - box.height / 2;
		box.immovable = true;
		add(box);

		pad = new FlxVirtualPad(FlxDPadMode.NONE, FlxActionMode.A);
		add(pad);
	}

	override public function update(elapsed:Float)
	{
		super.update(elapsed);

		FlxG.collide(box, sprite);

		var jumpPressed:Bool = pad.buttonA.pressed;

		if (jumping && !jumpPressed)
			jumping = false;

		/*
		 * Reset jumpTimer when touching the floor
		 * Note: This sprite's touching flags are set via FlxG.collide,
		 * and are reset to false on super.update
		 */
		if (sprite.isTouching(DOWN) && !jumping)
			jumpTimer = 0;

		if (jumpTimer >= 0 && jumpPressed)
		{
			jumping = true;
			jumpTimer += elapsed;
		}
		else
			jumpTimer = -1;

		// hold button to jump higher (up to 0.25s)
		if (jumpTimer > 0 && jumpTimer < 0.25)
			sprite.velocity.y = -300;
	}
}