Are you hoping to perform the FFT using OpenAL? I don't know if that's possible. Your code will likely be performing the FFT.
You don't need to explicitly set up any threads. However, your audio output library will probably do so on your behalf. I'm not familiar with OpenAL, but the way that a lot of audio libraries operate is by letting you specify a callback that will feed more audio into the output. Thus, your main program will load audio from the audio file, stuff it into a buffer (likely protected by a mutex) for the audio callback to read, compute an FFT over the audio window, and perhaps visualize the data for the user.
Again, the audio library will probably be managing the threading so you don't need to worry about the exact threading implementation or library. But be sure to manage shared data correctly with a mutex.