The chances of contacting bird flu from a properly cooked (above 100°C) chicken and egg are:

Bird flu is caused by avian influenza. The influenza can be found inside or on the surface of the egg. Heat is known to deactivate the pathogens and cooking at such a high temperature of 100°C and above helps in killing the strains of avian influenza.

Hence, the chances of contacting bird flu from a properly cooked (above 100°C) chicken and egg are negligible.