Friedman argues that the world has become increasingly globalized, taking away the inherent advantage of developed nations and equalizing the economic playing field. With the ease of globalized supply chains and communications, everyone in the world can compete for customers, regardless of location.
For education, the first thing this means is that it will need to be less parochial. Although English is a global business language, monolingual schools are still at a disadvantage, and students should be offered Mandarin, Arabic, Spanish, and other languages in order to be competitive with people educated to be bilingual or multilingual.
Next, he sees things like MOOCs becoming increasingly important as the internet makes it possible to gain a genuinely global education even from the convenience of one's home. The existence of high-quality online courses mean that brick and mortar educational institutions cannot be complacent; unless they clearly offer either a better price or a higher quality of education, they may see declining enrollments. Similarly, elite educational institutions, hampered by the nationalism of Trump's government and increasing restrictions on international students, may need to focus on building online and foreign satellite campuses in order to avoid becoming provincial backwaters.
Finally, students in the developed world will be competing for online or platform-mediated jobs with people who live in countries with lower costs of living, causing downward pressure on wages for an increasing number of jobs. This means that in order to justify the premium salary needed for a living wage in a developed country, students will need to focus on getting good credentials showing competitive skills in growing industries, rather than just having generic business degrees.
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.