How to find parent node using child node or attribute?

Assuming you have already created your XML object in Flash and have a reference to one of the children (<subVideo> tag in the example you provided) as either an XML object or XMLList object, you can call the .parent() method to get a reference to the parent of the <subVideo> tag and then call the .attribute() method passing "name" into the method call and it will return a String of "test". Below is the code example I created real quick. It assumes that you have an XML file named "test.xml" in the same directory as the FLA/SWF. The "test.xml" file I created for testing contains the exact example you provided.

import flash.net.URLLoader;
import flash.net.URLRequest;
import flash.events.Event;

var xml:XML;
var urlLoader:URLLoader = new URLLoader();
urlLoader.addEventListener(Event.COMPLETE, onFileLoad);
urlLoader.load(new URLRequest("test.xml"));

function onFileLoad(e:Event):void {
  xml = new XML(e.target.data);
  // xml.children() = XMLList object of the two <subVideo> tags
  // xml.children().parent() is, in this case, an XML object identical to the "xml" variable
  // xml.childnre().parent().attribute("name") returns the String value of the "name" attribute
  trace(xml.children().parent().attribute("name"));// returns String value of "test"
}

http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/XML.html

the parent's node name is video.

do you mean you want to get the node itself or it's id or name given a particular subvideo id or name or src?