I know how to play / blow a flute.

[emsr2d2]

Is 'the' optional?

Yes. The article is frequently omitted especially in phrases such as "My aunt plays violin for the London Philharmonic Orchestra".

[BobK]

Does it mean "Can you play a guitar?" is not natural? I remembered a native speaker asked me, "Can you play a guitar?'

It sounds very odd, as others have said. It would sound less odd (but still a bit dubious) if it was well known that you played the mandolin and somebody asked 'Can you play a guitar too?'. But I feel 'the' would be more natural. A better exception would be in types of guitar. 'Everyone knows you can play the electric guitar, but can you play an acoustic one?'

b

[BobK]

Is 'the' optional?

Apart from the case given by Ems (not talking about an ability but a position*), I would say it's traditional Br Eng rather than optional. 40 years ago I would have said 'I can play the guitar'; but today young people (exposed to the usage mentioned in my PS) often just say 'I play guitar'.

b

PS

* That 'position' can be professional (in an orchestra) or functional. At the end of a rock concert the lead singer might say 'Let's hear it for/Give it up for... [='Please applaud'] so-and-so on bass... [etc.]'