Never mind trapping.
Never mind zapping.
It's much more satisfying to hunt the annoying flies down one at a time and give them what they deserve.
Step 1: Choose Your Weapon
The weapon of choice for the seasoned fly hunter is the broad rubber band. Narrow rubber bands can work, but carry much less energy, so are more likely to simply scare the prey off. Like shooting at a tiger with a BB gun, although the fly is less likely to turn round and take your arm off.
When using the bands, the universally-approved method is to hook the band over the tip of the index finger of your favoured hand, and pull it taught with the other, so that the band will fly wherever you point, and you can even sight along your arm and finger.
However, there is still some debate regarding length - longer bands are heavier, but shorter bands travel more quickly.
Pith helmets are optional.
Step 2: The Hunt
You need to remember several things:
Be ready at all times.
You never know when the little devils are going to turn up, so keep your weapon at hand (or, more accurately, around your wrist).
You don't need to hide, but you do need to move slowly. The flies vision is keyed strongly to sudden, predator-style movements. Load your ammo as soon as you spot your prey, then move slowly, oh, so slooowly up behind the fly.
Take him from the rear
Flies have a weakness - due to their ornithopter-style flight, they always take off in reverse, no matter which way they want to go, or what they want to fly away from.
Shoot from behind the fly, and even if it sees the rubber band coming, it will actually spend a precious moment flying towards its own doom.
Move stealthily enough, and you will get surprisingly close to your prey. The closer, the better.
He's only playing dead
It is quite possible to render your prey merely unconscious - be prepared to finish things quickly. Give the coupe de grace with the heel of your shoe, or a second, point-blank shot, or scoop the body up on a piece of paper and move it quickly before it recovers.
Step 3: Keeping Score
The original Great White Hunters kept "score" with trophies - impressive sets of horns, hides, heads, even whole mounted corpses. Fills the walls of the Great Hall, what, gives the servants something to dust, eh?
Unfortunately, if you try and mount your trophies on the wall, somebody else will probably wash them off.
Instead, if you want to keep an indisputable score (as might be the case with siblings or flatmates), then I suggest keeping the corpses in a glass jar. With a lid (you never know when the sneaky blighters are going to wake up...).
But what if they're alive? Won't they escape next time I open the jar to add another trophy?
Quite possibly, but then you have the chance of another hunt. Oh, if you're really set on making sure they don't escape, then give the jar a mighty shake before you open it - that will stun any sneaky flies long enough to add another to your collection.
Now, you'll have to excuse me, I'm sure I can hear a distant buzzing...