I do not know that Friedman tells us how the flattening of the world will affect the US educational system, but he does tell us how it should affect the system.
He says that the educational system will need to be more flexible and focused on teaching people to be flexible. He says that whatever the schools teach will soon be obsolete in the new world so specific skills and such are not really what should be taught. Instead, what is needed is schools that will teach students how to think -- how to be creative and flexible.
I think this is the main thing that Friedman is saying about education. However, I suppose that you could say that he is also saying that the system will have to adapt to competition from other countries as students are more able to attend universities in foreign countries.