There is no doubt that the Fluenz nasal spray vaccine is kosher, for four key reasons.
First, the vaccine is taken for health reasons. We are in the habit of taking pills, regardless of whether they are life-saving, which have non-kosher ingredients in them all the time. Many capsules such as amoxil (a common antibiotic), and cough medicines, are made using non-kosher derivatives, but because they are for medicinal purposes rather than nourishment there can be leniency. This alone is enough to permit using the nasal spray.
Second, the product is not taken orally. This is another situation in which there is leniency in the halachah, which is also applied to the intravenous administration of food and drugs.
Third, gelatine in itself is a denatured product, which has gone through many processes, which make it very far from the original piece of pork it came from — another trigger for leniency in Jewish law.
Fourth, the gelatine is only one ingredient making up a small part of a complex formula, which may be another ground for leniency.
All these factors together are more than enough to make the vaccine absolutely acceptable without straining the imagination. I would consider anyone saying otherwise to be acting in the extreme.