I don´t have the info when the term "kinh" came into existence, and still have to search a bit more to find out. kinh is most likely derived by jing in chinese: Beijing (northern capigtal), Nanjing (southern capital).
basically the vietnamese people consist of 86% of ethnic kinh as majority and 14% of the ethnics as minority (54 groups such as Tay, Tai, Hmong, Hoa, Khmer, Nung, and many others).
who are the kinh people?
yes, Kinh means capital, here Hanoi city or more precise the Red river delta. the region is the place when the first Vietnamese settled down and cultivated the land. Unlike the Kinh, many other ethnics live in mountainous regions. So the kinh distinguish themselves from others by geographic locations. the Kinh live mainly in cities and coastal regions.
apart from that, the Kinh have different cultures and custom than other ethnics. so basically Kinh are sinized people. I understand, the recent genetic study of Harvard medical school shows the Kinh´s ancestors originated from Taiwan. our forefathers came to the present day Vietnam before 5,000 years ago. according to this study, the likelyhood is extremely high, the Taiwanese came as seafather and settled down in the red river delta. so Kinh people have chinese roots.
Also, the DNA study of the hospital Saint-Louis in Paris confirmed the assumption that the Vietnamese population has evolved from the tai/Indonesian and the southern Chinese population.
some studies show a different picture. the first Vietnamese originated from austronesians. they came from the western pacific. some genetic research show the Viet people have mixed with the mongolians, who came as settlers to Vietnam.
so, we don´t know for 100 per cent. Perhaps more future researches can bring more light into this.
Yes, the people of Gin/Jing;京 is Vietnamese migrants, who came to China hundreds of year ago. they belong to one of the recognised minorities in China.
yes, you are right at the last part. "Bắc Kỳ" is northerner.