So it's not the Accuplacer? That's been used at every community college I know of, and it has both multiple choice questions and an essay for writing (as does the SAT, and most community colleges will accept that in lieu of the placement test).
Anyway, it sounds like his anxiety is the bigger problem, then? I think he could get the help he needs with his writing at a community college remedial writing class (and a class like that would probably be set up to help kids who are anxious about having to write, too), but he can't get there without taking the placement test, and his anxiety about writing prevents him from doing that. So it's a catch-22 of sorts.
Is his therapist addressing his anxieties at all? Has he ever been tried on a low-dose anti-anxiety medication like xanax? Those medications got a bad rap because of their potential for addiction, but I know a number of people who found that a low dose for a temporary time period was really useful in helping them get past stumbling blocks like this. YMMV, of course, and I'm not a doctor...