Red flesh is one class of peach. The Chinese varieties are not found in the US but some common red-flesh US peach varieties are Indian Cling and Indian Free.

Scott

What does it mean by" one class "

I probably should have said one type of peach. Prunus persica, the peach, is one species and in it are several different types. Nectarines are another type, they are also prunus persica but are a particular genetic trait of that species. Red flesh is similarly a genetic trait found in some varieties of peach. There isn't just one variety of red fleshed peach, there are many varieties with that trait. None of the modern Chinese red-fleshed peach varieties can be found in the US, but other varieties with the red-fleshed trait can. The US varieties are children of peaches that came from China via Europe, all peaches originate in China.

If you want to learn more about the modern peach varieties in China, look at the book "The Peach: Botany, Production and Uses" in Google books, chapter 2 is on Chinese peaches. Some pages are not shown in the free preview but there is a fair amount available.

Scott