How long have people been giving each other the middle finger?

Hundreds of years.

"The middle finger is the penis and the curled fingers on either side are the testicles. ... The gesture is widely known to Americans as flipping the bird, or just giving someone the finger. The Romans had their own name for it: digitus impudicus - the shameless, indecent or offensive finger.

During the early part of the Hundred Years' War (1337-1453) England's most effective weapon was the longbow. You can't shoot the longbow without the middle finger. So, the French then started cutting the middle fingers of all bowmen they captured. In defiance, the English solders would show their middle fingers to the French before the battle as if to say that they could still shoot the longbow.

By the way, the longbows were made of English Yew (Taxus baccata), a type of tree growing in England and Western Europe. The words "plucking the yew" meant shooting the bow. Along with showing the French the finger, the English would yell "Pluck Yew" at them. Over the years, the pronunciation of the words changed slightly, and now these words, often accompanied by showing the middle finger for emphasis, usually get bleeped out during the TV broadcasts.

not long enough

Thousands of years. There's evidence it was used in the classical greek period.

Since the 1940's

Since the 1300's

For at least as long as I can remember. I'm 58.