In Flex, you access a private variable by calling it from within
that class. Remember, the "private" modifier means it cannot be
directly accessed outside of the class you declare it in (note I
say "directly accessed" you can indirectly access it via public
functions which I will show below).
Example:
declare your variable at the top of your class like this:
private var myVariable:String;
Then, inside one of your functions of that class, you can access
the variable and/or assign it this way:
public function changeMyVariable(value:String):void {
// sets the private variable to a custom string
myVariable="test String";
trace("myVariable is set to "+myVariable);
// sets the private variable to the argument passed in
myVariable = value;
trace("myVariable is now set to" +myVariable);
}