Is Dutch the same as Deutsch? And Flemish? Danish?

No. Dutch is not Deutsch: Deutsch is what Germans call German, and that is a different language. Still, the requests I receive show that quite a few people think a Dutch voice-over can easily record German, Flemish or even Danish. For those, you need a native speaker of that language.

To sum it up:

The Netherlands: the Dutch speak Dutch. We call ourselves Nederlanders, our country Nederland and our language Nederlands.

Germany: the Germans speak German. They call their country Deutschland and their language Deutsch. That word looks like Dutch, but it is not the same.

Belgium: in Flanders, the northern part of Belgium, people speak Flemish, which is actually Dutch. But it sounds clearly different from the Dutch spoken in the Netherlands, so for a Flemish audience you are better off with a Flemish voice.

Denmark: Danish has absolutely nothing to do with any of the above.