Were British infantry trained to shoot attacking aircraft with rifles?

Don't forget that early in WW2, a lot of WW1 thinking was still current, both officially and with individual officers/NCOs.

In WW1, rifles were used against aircraft; there were even special adaptations. Of course that was generally meant to be massed rifles. Th expected targets were also very slow aircraft by WW2 or even modern standards, but aircraft got a lot faster just prior to WW2 and armies always seem to train to fight the last war.

Coming to WW2, there were devices used to train riflemen in leading fast-moving targets, including (from their instructions) aircraft. This demonstrates that aimed rifle fire was still expected in an AA role.

To answer the 1st question:

Yes, this, has probably happened sometimes at Dunkirk since there were German airplanes and British riflemen there. Given their numbers, this might have been a frequent behaviour. However, this does not mean that this was the main issue that German airplanes had to face at Dunkirk.

The movie Dunkirk conveys the false idea of an empty beach on which soldiers were waiting passively, under fire, to be evacuated. The reality of Dunkirk is that:

• Beaches were full of men and material, including anti aircraft guns and machine guns that would be more effective than rifles at shooting down aircrafts
• There was heavy land fighting at the beginning especially, with the Germans trying to break through. They were repelled by French and British, and thus relied on the Luftwaffe

Well, the question in your title is not the question in the body...

But, for the question in your title, certainly the German army and air force wanted to do harm to those soldiers on the beach at Dunkirk. Of course. War.

The question of soldiers' obligations to (or prohibition from) shooting at airplanes attacking them is different. Given the general ineffectiveness of shooting rifles at airplanes (both inability to judge lead, and the small calibre making just very small holes in big sheets of metal), it'd be more sensible for people under air attack to get down and cover their heads.

Again, there are two fundamental reasons why shooting rifles at airplanes is not effective. (And, no, it's not so much that you'll miss and the slug will come down again...) First, it is insanely hard to judge lead time. This is why already anti-aircraft batteries operated primarily by humans do not hit so many planes. Second, even with large-ish calibre rifles, the little holes they'd make in nearly all parts of an airplane would be harmless. Sure, there are some spots that would really matter, but not so many... especially considering the typical armor-ing of vulnerable parts thinking of larger-calibre attacks.

But, sure, why not shoot at the enemy? I might not be able to resist, either, even though I have an idea of the probable futility. :)

I must admit that I'm answering this without specific knowledge of British WWII regulations, but here is an American manual of the era, check page 29 (by page number) / page 36 (of the PDF document). Troops under air attack would be expected to fire their small arms when ordered fire, or to hold fire when there were no such orders.

The alternative to shooting at aircraft is not shooting at aircraft. Reasons not to shoot at aircraft:

• Shooting at aircraft may reveal the position of the ground unit. Not an issue in a besieged port.
• Bullets fired up will come down, a mile or two away, and the shooter cannot effectively judge what they will hit. WWII military rifles had a caliber similar to medium machine guns, and those were used for indirect fire with appropriate sights.
• Much ammunition will be expended to little direct effect.

On the other hand, there may also be good reasons to shoot:

• A bullet might bring the aircraft down. A low-probability event for any one rifleman, but with many soldiers firing the odds add up. Medium machine guns were used for air defense at the time, and a rifle platoon could put as much lead in the air as a machine gun. For that matter, British fighters carried .303 machine guns, too. They would fire more bullets than any one soldier, of course.
• Many bullets, or just their muzzle flashes, might cause the pilot to abort the attack run, or fire from less-than-optimum range.

The firing pattern prescribed for the machine guns of the American quartermaster company would basically fill the air with bullets and hope that the aircraft runs into one, by pure chance. Individual weapons would simply add to the density of fire.

To answer the second part of your question, this WW2 British Army training film includes details of how ground fire from infantry should be directed at enemy aircraft. As you can see at about 20 minutes in, it shows section fire against a dive bomber. It gives no information about the effectiveness of such a defence, but it was certainly British Army doctrine to engage aircraft in such a fashion.