playing a/the flute

Either.

I think we need to know the context.

"I see a boy. The boy is playing a flute."

"I see a flute. A boy is playing the flute."

"I see a flute and a boy. The boy is playing the flute."

"I know a boy. He plays the flute."

Note that "the flute" can mean a particular flute, or that class of musical instruments known as flutes.

Thus, "I know a boy. He plays the flute."

Did ya get all the nuances that DD and Contrex pointed out, Tanguatlay?

Hi JTT

I didn't know that, what I thought was a simple question turns out to be quite a difficult one.

If you saw the flow chart [that we all have within our mental grammars] that determines article use, you'd be very impressed. There's a book called "Three Little Words; A, An, The". It's a very [VERY] detailed description of how and why we use articles.