Shotgun wing shooting, or trap, skeet, or sporting clays will be of little use for rifle shooting at moving targets. The only real application where shotgun target shooting was arieal gunnery in WWII, training bomber, and anti-aircraft crews to shoot their defensive MG's and cannons at flying aircraft, and learn the principles of lead.
And in that case, they had a steady supply of tracer ammo to help them. And the distances and speeds were great enough as compared to bullet velocities that lead matters.
And clay pigeons and birds generally fly faster than people on foot can move. And average shotgun pellet velocities are about half to a third of most centerfire rifle ammo.
When dealing with moving people on the ground, lead can become a factor, but generally at greater distances, like a sniper situation, and then you ought to know how to estimate and calculate your hold for such shots. (Here some kinds of longer range big game hunting might help.) Of course, in most places in the U.S., shooting people at that distance, no matter what the provocation is going to put you in legal hot-water, unless it's total anarchy, or a civil war here etc.
With your mention of the Greek riots, I'm guessing you're thinking more of a fluid defensive situation. A bit of lead can help, but at urban distances, or close combat, lead for bullet flight vs. movement of a target on foot is not really a factor. What you're trying to lead is YOU. You're leading not to get bullet and target vectors to intersect, but to get ahead of your reaction time.
As others mentioned, the professional schools are open to civilians, such as Gunsite, Thunder Ranch, Valhalla, Blackwater, SIG, and others have rifle/carbine classes with "Hogan's Alley" type moving targets, simulated buildings, windows, and doors.
There's not much in the way of moving targets, (but USPSA (IPSC) and IPDA, and "Three Gun" matches (Rifle/Carbine, Shotgun, and pistol) have you doing lots of running, moving, and shooting from and around cover at multiple targets. And sometimes there are targets that need to be shot in order to release or expose others, or one that swings back and forth.
