I would imagine this would be something that Google would be skittish to get into. Flu symptoms are a) common and b) well known. Tracking symptoms of arbitrary potential epidemics could be very difficult to design, let alone verify, and there's little benefit to Google. Not even PR if they raise a false flag.
Tracking symptoms of arbitrary potential epidemics could be very difficult to design
Does it need to be terribly precise, though?
If, for example, lots of searches spring up for vomiting or sweating in a small radius, I'd imagine that'd raise a "Hey, you might like someone to look at this flag," which could be useful - just as long as the computers aren't shouting all day long.