To clarify, the way I was taught when I was officiating KY middle and high school games in the late 90s was there is some discretion.
If a player fumbles or taps the ball to then gain possession, it is not a dribble. In some cases (as you describe), if the player exhibits clear control with a single handed catch and dribble motion, then that is a dribble. So, if the player in that scenario stops dribbling and restarts, it is a double dribble.
In that clip, I would've given Flagg the benefit of the doubt and called that a deflection and no dribble. I really hate it b/c I would rather it be that any Duke player is screwing up.
Regardless, it is fun to actually chat/engage about calls, etc., so I appreciate the fact that we could do so without so much of the nastiness that is often on this board...so, kudos to you.