AS3 text linkage to xml

You have several problems in your code:

You don't wait for XML, and start ENTER_FRAME with access to myItems

There is no sense in additional information in the XML, because you apply same texts to the both fields.

function onMoveTexts(e:Event):void {
    my_text.x -= scrolling_speed;
    mySmallTextField.x -= scrolling_speed2;
    if (my_text.x < -my_text.width) {
        my_text.x = stage.stageWidth;

        if (myItems != null) {
            //Set next text
            if (++position >= myItems.length()) {
                position = 0;
            }
            my_text.text = myItems[position];
        }
    }

    if (mySmallTextField.x < -mySmallTextField.width) {
        mySmallTextField.x = stage.stageWidth;
        if(myData != null){
            mySmallTextField.text = myData.anotherData.info;
        }
    }
}

Or start your loop after you get XML:

function onComplete(e:Event):void {
    myData = new XML(URLLoader(e.currentTarget).data);
    myItems = myData..item;

    //add the listener to scroll
    addEventListener(Event.ENTER_FRAME, onMoveTexts);
}