pasture flocks and herds?

No, in fact, i would say that pasture is the best word for what you want to describe. I would put a comma between pasture and flocks, though: pasture, flocks and herds.

I tried to translate it into English like that:
In the early third century B.C., The Dingling , the ancestor of Uygur, started to pasture flocks and herds in the area north of Lake Baikal.
Is it OK?

I see now--pasture is a noun, but these days, it wouldn't surprise me to see it used as a verb. I'll go look.

OK, i find it listed as a verb, so that sentence works.

However, i would advise that you write "the ancestors of Uygur" as both Dingling and Uygur are collective proper nouns. So, for example, i would write "The Belgae, one of the ancestors of the Britons . . . " because Belgae is a collective noun.

A guy who tells us he grew up in a family that raised a lot of their own food doesn't know that 'pasture' is a verb. Strange days indeed.

It's kind of transatlantic.

We'd probably use the old word graze.

I don't think it's "transatlantic," i believe that most Americans would also use the verb to graze.

I'd say that 'pasture' is the better of the two [the other of course is 'graze'] because it also has the feeling of 'tend'.

They probably thought pasture-ised milk would be more healthy.

Of course, you can stable a horse, hammer a man, bed a woman so it's not too much of a stretch to pasture a herd.
Even if it is a bit poncey.