What message might the Nazis have wanted to communicate by including several different Nazi flags on the poster? What message is conveyed by showing the eagle clutching a swastika with its talons?

This question is very interesting because the eagle was not created by the Nazis, but they imitated the meaning that they assign to this eagle in Rome.

This is why many know it as a Roman eagle and later it was used as an icon with the Nazi symbol.

the Roman eagle, used by the Emperors of the Holy Roman Empire and in the modern coats of arms of Germany, including those of the German Confederation, the Second German Empire, the Weimar Republic and the Third Reich.

Before the German Empire this eagle was double-headed. During the Third Reich, the German eagle was combined with a National Socialist style swastika. Before it was used as a symbol for Nazi Germany, the eagle was used by the Weimar Republic as a national insignia. Today, the Reichsadler is still part of the coat of arms of Germany, renamed Bundesadler (Federal Eagle)

Explanation:

The eagle we write was used in many countries, an early representation of a double-headed eagle on a heraldic shield, attributed to Frederick II of Hohenstaufen, found in the Chronica Majora de Mateo de Paris (ca. 1250). The Armorial (ca. 1280) also shows the double-headed eagle as the coat of arms of the King of Germany.

The eagle itself is one of the animals that flies the most, has the most power, and is most fearsome. As for the use of such an animal in a symbolism, it seeks to represent the strength and greatness with which the Nazi symbol expanded at that time.