Well,that is the flag used by the Chinese during the invasion of USA,but is the only chinese flag used in fallout universe,so that is it
And I agree with you about the American-Soviet relations,because China have more population than USSR+USA,so if they became the world greatest power,both Soviet Union and USA will fear them,so I guess that Soviet Union maybe still have bad relations with NATO,but they shall be persuing a "good neighbour" policy with USA,trying to bring them to the table to weaken china