Well...
To be frank, stockpiling a marginally effective medication that is mainly a symptom suppressor is not a good idea.
You can, quite literally, play soccer with a H5N1 infected bird and not become infected, unless you have a weakened immune system or don't shower afterwards for a week or so. I've personally handled six confirmed-infected birds from our area without protective clothing, and not a thing happened.
My doctor agrees with me on this: The Bird Flu Scare is just that, a scare. If Bird Flu scares you, why aren't you continually doped up on antibiotics in case you get the plague? Because plague is far more likely than the (relatively benign) H5N1.