A2 is setting a screen for A1 on B1. A2 really lays the shoulder into B1. What thought process do you use to determine if you are going to call an intentional/flagrant foul? Am I even allowed to call an intentional for this described play?

My two cents--

If you believe that A2's contact was "excessive," an intentional personal foul is an appropriate call.

If you believe that A2 was intending to hurt B1, then a flagrant personal foul is an appropriate call.

Whether your play falls into either of these categories is a "had to be there" situation.

Sure, you're allowed to call an intentional or flagrant on any type of play. But, in my experience, I've never seen an intentional foul on a screen. I think it would have to be so obvious, like throwing an elbow instead of a shoulder, before I'd consider an intentional. Or else maybe if the screener had his arms crossed and then raised them, pushing his forearms into the defender's throat. Something like that might get me to think about an intentional.

But lowering the shoulder, while obviously a foul, doesn't seem to be a "hard foul" or flagrant.

What makes you ask this? Did you see a play that made you think it might be intentional? If so, I'd be interested in the details.

A2's upper torso turned about 45 degrees on the screen. As soon as I blew my whistle, even his coach was yelling at him that it was an absolutely stupid foul.

The kid has a reputation for cheap shots in the league. This one was just really blatant. I don't think he was trying to hurt the other kid, but definitely wanted B1 to know he was picked.

While I've never had to call an intentional or flagrant foul on a screener, I have called an intentional on the player being screened. The defensive player didn't even try to go around the screen; he just took both hands and shoved the screener in the chest, which sent him flying.