What exactly do you mean by "flow across the Chinese border"? It's my understanding that all electronic USD are in the USA, either directly in the central bank or indirectly through another bank which has an account in the central bank. They can't actually flow out of the country, except as cash.
China controls the use of CNY to buy non-domestic things, particularly foreign exchange. Domestic companies and savers‘ “movement” of the currency is tightly controlled, and the government has immediately tightened the screws on everyone before.
USD is not controlled in this manner, which makes it pretty easy to obtain. One of the important features of a reserve currency is easy obtainability and convertibility, but this runs counter to China’s internal stability goals.
