Don't have this season's info yet but last year, 2011-2012 season, there were six contracted manufacturers who provided U.S. vaccines. None in China.
The manufacturers licensed to produce the nation’s 2012-2013 flu vaccines and the brand names of the vaccines for the upcoming flu season are: Afluria, manufactured by CSL Limited;
Fluarix, manufactured by GlaxoSmithKline Biologicals;
FluLaval, manufactured by ID Biomedical Corporation;
FluMist, manufactured by MedImmune Vaccines Inc.;
Fluvirin, manufactured by Novartis Vaccines and Diagnostics Limited;
and Fluzone, Fluzone High-Dose and Fluzone Intradermal, manufactured by Sanofi Pasteur.
OK, seems to be the same ones this year. And a correction: it is two A strains and one B.
To add to this toxic brew of discussion, note that as far as drug companies go, manufacturing vaccines isn’t particularly high on their list of things they want to do. Profit margins aren’t very good, and the potential liability (from lawsuits, justified or not) is off the charts. It’s a shame that this has been allowed to occur.
A good primer on this is to research the history of the Polio epidemics that were once common in the US - the Salk and Sabin vaccines, initially had some problems - and in some cases iirc from my reading of history, recipients contracted Polio who were otherwise healthy.
The wind up to all this, it’s doubtful a Polio vaccine introduced now would pass muster these days? I dunno.