Order of operatiosn for visa required international (PVG) travel
My advice would be to go to the embassy's website and read, reread, and reread the visa application information. If the application says to show up with a copy of your itinerary or asks for flight and hotel information, provide it. I think that as a relatively routine US applicant for a Chinese tourist visa, you should be fine booking the flight and then applying for the visa, but don't take my word for it; check with the embassy directly.