Flipping is more common than giving...
'Bird', meaning the middle finger, is first recorded in
Current Slang, published by the University of South Dakota in 1968. The only logical reason I can see for that is the fact that a hand with the middle finger raised might be thought to have a bird-shape...ie the head and neck outstretched like a duck in flight and the 'wings/body' formed by the other four digits.
The 'flip' element was added later to suggest the finger has imparted to it an appropriate up and down movement to simulate the activity it describes!
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