Friedman quotes Indian IT entrepreneur Rajesh Rao as stating "We can't relax. I think in the case of the US this is what has happened a bit."
If the US is doing this, why does it impact the flattening of the world
Assuming that Rao is correct and the US has "relaxed," this helps to "flatten" the world because it gives people in many other countries the chance to gain market share by trying harder than Americans who have become complacent.
Rao makes the point that his software company got ahead through hard work and constantly reinventing itself. In the pages before the quote you give, he lists a Dhruva 1.0, 2.0 and 3.0. All of these came about as the company worked hard to become whatever was needed. He argues that people in India and other countries that are not as rich as the US or Japan or places like that are simply "hungrier" and will therefore work harder.
If this is true, it "flattens" the world by giving more startups in more countries an opportunity to compete. This globalizes the economy and flattens the world.