No one knows the answer to this for sure, and it seems likely that the answer is different for different Americans.
The flattening of the world brings American companies and workers into competition with foreigners. This is, of course, detrimental for those companies and workers who get outcompeted. Americans who used to work in call centers, for example, are hurt as their jobs are moved to India or the Philippines as a result of the flattening of the world.
However, at least in theory, this flattening should be good for the US. The US workforce is more educated than that of many other countries. Therefore, the US should be able to adjust to a globalized economy and shift resources from older industries that are being outcompeted to those that are newer and more competitive.
This is clearly a challenge for the US and no one can know for sure if it will ultimately end up being a good thing for the country.