I was going to say that in the U.S. we would simply say "the first flute" (rather than "the first flautist") but it is complicated! Looking at the web pages of the New York Philaharmonic and the Boston Symphony and a few others, I see that I am wrong. The correct formal name for the position, according to these orchestras, is "principal flute."

Yes, "first flautist" seems to be the standard expression - see http://www.linguee.com/english-german/search?source=auto&query=first+flautist