I decided to look up the history of the symbology. Interestingly, the sketch this flag is based on came from Ben Franklin. He did not use it as a symbol of independence, rather a call to come together.:
Benjamin Franklin is famous for his sense of humor. In 1751, he wrote a satirical commentary in his Pennsylvania Gazette suggesting that as a way to thank the Brits for their policy of sending convicted felons to America, American colonists should send rattlesnakes to England.
Three years later, in 1754, he used a snake to illustrate another point. This time not so humorous. Franklin sketched, carved, and published the first known political cartoon in an American newspaper. It was the image of a snake cut into eight sections. The sections represented the individual colonies and the curves of the snake suggested the coastline. New England was combined into one section as the head of the snake. South Carolina was at the tail. Beneath the snake were the ominous words "Join, or Die."
This had nothing to do with independence from Britain. It was a plea for unity in defending the colonies during the French and Indian War. It played off a common superstition of the time: a snake that had been cut into pieces could come back to life if you joined the sections together before sunset.