We don't catch bird flu from eating infected birds, we catch it from being exposed to live birds who are sick (or to their droppings, as I understand it).
You would need to obtain a sufficient viral load in order to be infected. One or two copies won't do the job, you'd need to ingest infected material in some manner. Eye splash, breathe dust from cleaning a chicken house, or vicsera that harbor many copies of the virus. This is why we throw the guts out of most things before we continue preparation.
The position known since the Kama Sutra as the Aztec Sacrifice. However, in the next edition it will be renamed the "Praying Mantis" in order to be less offensive.