There's an important press release from the medical boards of Food Allergy and Anaphylaxis Network (FAAN) & Food Allergy Initiative (FAI) about egg allergies and flu vaccine:
"The yearly flu vaccines are recommended for all children over age 6 months. These vaccines contain a very small amount of egg protein, and this raises concerns about giving them to children with egg allergy. For many years, physicians and various medical societies and expert panels recommended avoidance of these vaccines in children with severe egg allergy. This thinking has been changing."
Read more at Food Allergy Initiative's (FAI) site.
As an asthmatic, who's non-egg allergic, I get the flu vaccine every year, without issue or allergic reaction. Talk to your medical provider about what is best for you and your family.