Hi Jillius
I have Psoriasis, on my lower legs knees and elbows, with odd bits on my forearms and thighs.
I have 3 tattoos (upper arm, shoulder and ankle), i got them several years ago and none of them caused a flare up with Psoriasis.
I have been contemplating getting another but am a bit conscientious in case it flares up this time. I have just clicked on the link from octavius and i never realised that there was actually a medical term for the flare up of psoriasis due to damage on the skin.
To your original question, as long as the tattooist isn't actually tattooing over a patch of psoriasis then i can't see why they'd not do it.
I guess there is no set rules as to how a tattoo might affect you, and its up to you if you want to have one and risk a flare up.
Good luck, i hope if you do get one you don't get a flare up..........or whoever is thinking of it.