NOT A TEACHER
I think that with "the" it's a general statement, it refers to one's general ability to play a particular type of instrument. 'I play a flute' is an unusual statement (and I don't think I have ever heard it). It means to me that the speaker only plays one specific flute.
I don't deny that sometimes our constructions are not logical. For example:
I can drive a car.
I can play the flute.
My brother learnt how to drive a lorry when he was 17.
My sister plays the drums, the clarinet and the guitar.
Can you drive?
I have a licence to drive a car, but not a motorobike.
Obviously, when we say "I can drive a car" we don't simply mean we can drive one car but not any of the other millions of cars in the world. My brother didn't learn to drive only one lorry.
However, those are the terms we use and no, I can't explain why.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.