The simplest form of collision is 1-to-1 collision. You call FlxG.collide(), optionally setting a callback to trigger when collision happens.

// checks if 2 objects collided, and calls the function `callback` if they do
FlxG.collide(objectA, objectB, callback);

Demonstration

package;

import flixel.FlxG;
import flixel.FlxSprite;
import flixel.FlxState;
import flixel.util.FlxColor;

class PlayState extends FlxState
{
	var spriteA:FlxSprite;
	var spriteB:FlxSprite;

	override public function create()
	{
		bgColor = 0;

super.create();

		spriteA = new FlxSprite("assets/sprite.png");
		spriteA.x = 24;
		spriteA.y = FlxG.height / 2 - spriteA.height / 2;
		add(spriteA);

		spriteB = new FlxSprite("assets/sprite.png");
		spriteB.x = FlxG.width - 24 - spriteB.width;
		spriteB.y = FlxG.height / 2 - spriteB.height / 2;
		add(spriteB);

		spriteA.velocity.x = 150;
		spriteB.velocity.x = -150;
	}

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

		FlxG.collide(spriteA, spriteB, collision);

		if (spriteA.x <= 0)
			spriteA.velocity.x *= -1;
		if (spriteB.x >= FlxG.width - spriteB.width)
			spriteB.velocity.x *= -1;
	}

	function collision(spriteA:FlxSprite, spriteB:FlxSprite)
	{
		spriteA.velocity.x = -150;
		spriteB.velocity.x = 150;
	}
}