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Description
This is in fact the Wehrmacht eagle, which was somewhat similar to the eagle of the Weimar Arms except that it stands on a swastika. As he noted, this eagle was to be seen on the steel helmet as worn by the Army and Navy (though not by the Luftwaffe or the Waffen-SS). It was a shield-shaped badge (dark green background, white eagle) worn on the left side of the helmet; a shield with diagonal stripes of black-white-red was worn on the right side.
The "National Eagle" —or a version of it— was worn over the right pocket on Army and Navy uniforms and also as a cap badge. This was the more familiar style with spread wings, standing on a swastika within a wreath. The Waffen-SS wore a similar-but-not-matching eagle on the left sleeve, and the police had still another type.
There were quite a few different patterns of Nazi eagles. Some were Party badges, some were strictly military, while others were national symbols, e.g. the version used on the Government Authorities flag [Reichsdienstflagge]. But the one you refer to as the "National Eagle" was in fact reserved for the armed forces. It was applied to Hitler's Führer standard because he became the Supreme Commander of the Armed Forces after the death of old President von Hindenburg in 1934 and his assumption of the powers of the presidency as Führer and Reich Chancellor.

Description
This is in fact the Wehrmacht eagle, which was somewhat similar to the eagle of the Weimar Arms except that it stands on a swastika. As he noted, this eagle was to be seen on the steel helmet as worn by the Army and Navy (though not by the Luftwaffe or the Waffen-SS). It was a shield-shaped badge (dark green background, white eagle) worn on the left side of the helmet; a shield with diagonal stripes of black-white-red was worn on the right side.
The "National Eagle" —or a version of it— was worn over the right pocket on Army and Navy uniforms and also as a cap badge. This was the more familiar style with spread wings, standing on a swastika within a wreath. The Waffen-SS wore a similar-but-not-matching eagle on the left sleeve, and the police had still another type.
There were quite a few different patterns of Nazi eagles. Some were Party badges, some were strictly military, while others were national symbols, e.g. the version used on the Government Authorities flag [Reichsdienstflagge]. But the one you refer to as the "National Eagle" was in fact reserved for the armed forces. It was applied to Hitler's Führer standard because he became the Supreme Commander of the Armed Forces after the death of old President von Hindenburg in 1934 and his assumption of the powers of the presidency as Führer and Reich Chancellor.