Flemish vs ethnic group

Flemish and ethnic group both are nouns.

Word	Noun	Adjective	Verb	Adverb
Flemish	Yes	Yes	No	No
ethnic group	Yes	No	No	No

As nouns, ethnic group is a hypernym of Flemish; that is, ethnic group is a word with a broader meaning than Flemish:

Flemish: an ethnic group speaking Flemish and living in northern and western Belgium
ethnic group: people of the same race or nationality who share a distinctive culture

Other hypernyms of Flemish include ethnos.

Flemish (noun)	ethnic group (noun)
one of two official languages of Belgium; closely related to Dutch	people of the same race or nationality who share a distinctive culture
an ethnic group speaking Flemish and living in northern and western Belgium

Flemish (adjective)	ethnic group (adjective)
of or relating to Flanders or its people or language or culture