While I do think that some viral and bacterial infections come into the US via illegal aliens and also unvaccinated US citizens who travel abroad and come home and bring back diseases like Measles.
https://www.dailynews.com/2015/02/04/disneyland-measles-outbreak-dwarfed-by-2014s-in-ohios-amish-country/
But influenza is not one of them. Influenza has been around and has killed many millions long before illegal immigrants to the US started arriving.
http://www.influenzavirusnet.com/history-of-influenza.html
You could stop all illegals from coming into the country but would still have influenza outbreaks.
Flu is transmitted by poor hygiene habits. Adults who do not wash their hands spread the flu.
US vaccines are not directed to strains of flu expected to occur in 3rd world shitholes.