That depends a great deal on what you mean by "branch," since most magickal traditions can be traced back to very primal and ancient religions, evolving the entire way.
For exameple much of modern Hermetic magick views itself as a continuation ancient Egyptian mysticism, which would make it around 5,000 years old, give or take a few hundred years. Another way of measuring the age of Hermeticism is to trace it back to the works of Hermes Trismegistus from around 200-300 AD. Or you could trace it back to when the works of Hermes Trismegistus began being used by alchemists and other folk we might actually recognize as magicians - this occurred during the rather large span of time that made up the Middle Ages from 400 to 1,500 AD. Or you could trace it back to the founding of loosely formed Hermetic traditions (as opposed to a smattering of Hermetic texts) like the Rosicruician order in 1407.
Depends on how you define "branch of magick." The Chinese used oracle bone divination a good 10,000 or so years before the Egyptians developed anything more than the most rudimentary of spiritual practices.
Witchcraft has been with us since the dawn of time. There is no way to construct a complete history of Witchcraft, simply because we do not understand how ancient people saw their world. my personal theory is that they, becuase they were the first beings, were so close to the earth they could feel the energy that everything has, and they learnt how to manipulate that. When people looked at their world with wonder about how things happen, the first Gods and Goddess' were born.
As language developed, it allowed people to share abstract concepts, such as Deity. It could very well be that after words for danger, or food, some form of God or Goddess may have been next. We really have no way to ever know for sure, but it makes sense that important concepts were the first to be labeled in some way. We humans have always had a need to understand the world around us. We are curious, and inventive. We want to know why things are the way they are. The Priests and Shamans of ancient cultures were the first scientists. They gave explanations as to why the streams flowed, seemingly never ending in some places, or why they dried up in others. They explained how light from the sky caught the forest on fire. They explained the lights in the night sky. They were all the work of Gods. Over time, people understood that certain things were certain ways. There were patterns to the seasons, and the stars in the sky. There was order in the universe, and it was all by Divine Plan. Gods ran everything. A God caused the sun to rise and set, a Goddess made the animals fertile. The Gods of the Sun and the Moon looked down upon their people.
Each culture had created Gods that suited them. The Greeks had gods that were philosophical and contemplative. The Romans put their Gods in an orderly pantheon. The Norse had rough, coarse Gods. Each culture made their Gods in their own image, even the Christians. By the Middle Ages, these Gods and Goddesses were well established.
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