what is the best organic way to get rid of blackfly on my artichoke?
in the event of there being no avian assistance available, wash them off with a hose
You could spray them with a soapy solution - just mix up some fairy liquid (other detergents are available) and water slightly stronger than you would use for washing up (I'm assuming that you do wash up) put it in a spray bottle and spray over the pesky little blighters. I usually do this after I've either sprayed them off with a hose (I had thousands on my cherry tree at home) or rubbed them off by hand (no hose at the allotment). Rubbing them off does leave your fingers covered in a sticky residue. The spray is good at removing this too!.
For a truly organic solution you could grow Tumbling Ted (soapwort) and leave that in some water for a few days to make the spray. It does work and you get the benefit of hundreds of beautiful, tiny, pink flowers in spring.
You could also buy some ladybird larvae (easy to get hold of online) and release them near the blackfly. They will munch on thousands of them and keep munching after they've turned into adults. If you choose this option check for ants first as they farm blackfly (literally - they will move them to plants that aren't infested) so will kill any predators.