If the variable is already declared, you can use bracket
notation to get a reference to it:
public var piece:String = "";
public var ref:String;
private function myFunc():void
ref = "piece";
this[ref] = "door";
should display "door in your binding.
You can not "create" a var using bracket notation because
Application is not dynamic. If you need this, create an Object, and
add a reference to that.
var oMyObj:Object = new Object();
oMyObj[ref] = "door";