Christina,
OK, now I am confused on what you are missing then... When you publish your FlexViewer to the web you copy the contents of the bin-release to your web folder and as you mentioned you see an index.html in that folder. The index.html is the main web document for your FlexViewer web page so if you want it to have a favorite icon than you have to add the line of html code to the header section of the index.html. If you are asking about having your development environment where to put that line than it is in the index.template.html in the html-template folder of your FlexViewer project.