It is not possible to grow chicken eggs faster. So it's been impossible to have anything less than a years lead time to get flu vaccines made in sufficient quantities.
Planet money even did a show on the emergency chickens [1] (have they been called into service already ?). So we have the chickens, but no COVID vaccine that can be grown in eggs.
[1] https://www.npr.org/2020/03/13/815307821/planet-money-why-th...