We tried calling Palo Alto Medical Foundation (the DMV of health care). If you can ever get through the phone tree, they'd be glad to have you explain to them what Flumist is, transfer you to six other people, then tell you they don't have it.
If you haven't heard of it, Flumist is a flu vaccine nasal spray. It's an alternative to the flu shot. Good for kids who hate getting shots. Seems to provide comparable protection to the flu shot.