To add a UIComponent as a child of another UIComponent you can use addChild():
myComponent.addChild(myOtherUIComponent);
However, a validator is not a UIComponent or DisplayObject. It does not get added as a child to a page. If you are just replacing the fx:Declaration
piece of an MXML file with an ActionScript piece that does the same thing, then you don't have to do much more.
I would make the lengthTextValidator a public, or protected, instance variable on the component:
public var lengthTextValidator:StringValidator = new StringValidator();
That means the variable will be use within the component. Your original syntax without the public or private will either make a method specific variable that won't be accessible when the method is done executing or will put the variable in the internal namespace.
The rest of your code must go in a method. For an ActionScript class; you can put it in a constructor. Or for a MXML class you can put it in an initialize or creationComplete event handler.
lengthTextValidator.source = fieldTextInput;
lengthTextValidator.property = "text";
lengthTextValidator.required = true;
If you are putting the validator code in a separate class; then you'll have to import the class and create an instance of it:
import myPackage.MyClass;
public var myClass :MyClass = new MyClass();
Then you can access the validator by accessing the public variable on the component:
myClass.lengthTextValidator;
Finally; if you just want to move that snippet into an ActionScript file that is not a class; you can use the include directoive inside a fx:Script block:
<fx:Script><[[
include "myASFile.as"
]]></fx:Script>
The last approach is unorthodox and not usually recommended.