The double headed eagle is actually the Phoenix bird of ancient Egypt.
Originally Posted by Toddy
From The Phoenix: An Illustrated Review of Occultism and Philosophy By Manly Palmer Hall,
"Among the ancients a fabulous bird called the Phoenix is described by early writers ... in size and shape it resembles the eagle, but with certain differences. The body of the Phoenix is one covered with glossy purple feathers, and the plumes in its tail are alternately blue and red. The head of the bird is light in color, and about its neck is a circlet of golden plumage. At the back of its back the Phoenix has a crest of feathers of brilliant color ...
The Phoenix, it is said, lives for 500 years, and at its death its body opens and the new born Phoenix emerges. Because of this symbolism, the Phoenix is generally regarded as representing immortality and resurrection ... The Phoenix is one sign of the secret orders of the ancient world and of the initiate of those orders, for it was common to refer to one who had been accepted into the temples as a man twice-born, or reborn. Wisdom confers a new life, and those who become wise are born again."
Hall also stated that the eagle also represents the Phoenix.
Again Hall-"These were the immortals to whom the term 'phoenix' was applied, and their symbol was the mysterious two-headed bird, now called an eagle , a familiar and little understood Masonic emblem ."
And Albert Pike-"... the Eagle was the living Symbol of Egyptian God Mendes ... and the representative of the Sun ..."
You can trace the five pointed star to ancient Egypt as well.It is also described as the blazing star representing Sirius the dog star.
Symbols sometimes have multiple meanings in Occult tradition.They are often sigils in alchemy and "magick"