You can use Bitmap Fonts with the FlxBitmapText object. You have to create and pass a FlxBitmapFont, which you can create in a number of different ways, such as AngelCode.

// creates a new FlxBitmapText, using a monospace 8x8px font.
text = new FlxBitmapText(FlxBitmapFont.fromMonospace("assets/tiny-font.png",
	FlxBitmapFont.DEFAULT_CHARS, FlxPoint.get(8, 8)));

// set the text's text to "Hello, World!"
text.text = "Hello, World!";

Demonstration

package;

import flixel.FlxG;
import flixel.FlxState;
import flixel.graphics.frames.FlxBitmapFont;
import flixel.math.FlxPoint;
import flixel.text.FlxBitmapText;

class PlayState extends FlxState
{
	override public function create()
	{
		bgColor = 0;

super.create();

		var text = new FlxBitmapText(FlxBitmapFont.fromMonospace("assets/tiny-font.png",
			FlxBitmapFont.DEFAULT_CHARS, FlxPoint.get(8, 8)));
		text.text = "Hello, World!";
		text.scale.set(2, 2);
		text.screenCenter();
		add(text);
	}
}