Here is a nice post by 9media.com regarding the text drag, where you can find the source code that enables you to do it. This feature is missed in the Flash Plugin, so for sure it will be a nice resource for you.
Source | Draggable text selection in AIR with AS3
About the Author: Carlos Pinho
A father, a husband and a geek... Carlos was the founder of projects like The Tech Labs and Flash Enabled Blog. He is the founder of TekTuts He is passionate about technologies. Their main skills are in analytics, transport & logistics, business administration. He also writes about programming resources, trends, strategy and web development.