Uhh, well, first of all, it's unlikely you could find a vet that would readily give you that. You'll need a lot of money, and even so, no doctor would want to put their own future on the line like that, it's a big crime to illegally assist in suicide. They'd likely report you, which would make volunteering at one of those places difficult. Not to mention that you'd need to have some kind of experience/education. On top of that, death by pentobarbital takes about 15-30 minutes, and the symptoms of overdose aren't that pleasant.
SN is more accessible, more peaceful, and less complicated than this..