To put it in a simple way, to express the English 'of', there can be two cases: 1) no article, as most of the countries, all towns, names etc.: von die Flagge von Deutschland, der Eiffelturm von Paris, das Auto von Hans 2) with article, as some countries like die Schweiz, die USA, die Türkei and all other nouns: die Flagge der USA, das Auto des Nachbarn etc.

The constructions are a bit different. The first one (with a dative, yes) is literally rather "the flag of Germany" than "Germany's flag" - German has these two constructions too, the latter would be "die Flagge Deutschlands", with a genitive just like in your second example. Things get a bit complicated there because "Schweiz" is one of the country names that are always used with an article, therefore the genitive is "der Schweiz". (The "von" construction, "die Flagge von der Schweiz", is avoided in this case.)

The second sentence is genitiv.The Flag of Switzerland........here Schweiz is one of the countries which is feminine."Die Schweiz".Therefore genitiv form for feminine is der.Masculin and Neutral are "des".Feminin and plural are "der"................Even i'm an intermediate German learner.This is my understanding of the subject.Native speakers and the questioner,please forgive me if i'm wrong.

The second sentence is genitiv.The Flag of Switzerland........here Schweiz is one of the countries which is feminine."Die Schweiz".Therefore genitiv form for feminine is der.Masculin and Neutral are "des".Feminin and plural are "der"................Even i'm an intermediate German learner.This is my understanding of the subject.Native speakers and the questioner,please forgive me if i'm wrong.

I think the 2nd sentence doesn't have a literal translation to say "the flag OF Switzerland". The "der" is part of the word for Switzerland.