Where can I find hemagglutination inhibition (HI) assay data?
I don't think there's any universal database containing ongoing, widely representative HI assay output. The Antigenic Cartography group has made available some historical datasets that were used in published articles, such as 


Influenza A/H3N2 data published in Smith et al. 2004. Science 305:371-376
Data from H1N1pdm09 assays in 2009/2010 (click on the links for html/Excel/OpenDocument tables)
Data published in Koel et al. 2013. Science 342:976-979


Trevor Bedford et al. make their large set of historical HI data described in Integrating influenza antigenic dynamics with molecular evolution available in DataDryad.