!Note - in English all countries and adjectives describing the products, people or services from that country are proper nouns and as such start with a CAPITAL LETTER.
For example: Ireland - Irish, Belgium - Belgian
!Note - the Capital City of a country is the most important town or city of a country and it is usually the seat of government and administrative centre, the place where the leaders of a country or state meet and work.
Flags when describing the flag of a particular country you use the adjective that describes nationality.