Why cockpit? There is no interconnection to the outside in the cockpit. Open cockpit window? Better do not (at least not in the air). The only way "something" could come inside would be a bird strike in the bleed system, where it is highly unlikely that great amounts of viruses enter.
Bird flu is mainly a problem in bigger migrating birds, like Swan, goose and the like, which are rather seldome involved in bird strikes. Intesive studies in "contaminated" Europe have found that small birds, are not (yet) carrying H5N1.
There might be a potential risk for the Engineer when he touches remains of birds, but normal hygieny (wearing gloves, using soap, washing hands) should do the trick.
Dani