How does a steady wind flow generate sound?

The full description of viscous fluid flow (i.e. the Navier-Stokes equations) is non-linear and can be sensitively dependent on initial conditions. What this means in practical terms it that you can't always count on your intuition.

The evolution of the Kármán vortex streets linked by mbq from laminar flow around an obstacle are are a classic demonstration. (And easy enough for a determined middle school student to create in the garage for a science project, though things are likely to get wet...)

Any way, once the wind starts doing non-linear things, it can generate periodic stresses, and from that you get the whistling or humming noise we all know and love. Add a resonant cavity and you can amplify nice pure tones which is the short-short version of how this works in wind instruments.

There are really two parts to your question. First, how does the wind affect the motion of the paper, and how does that motion then couple to the behavior of the wind?

For the case of a flag fluttering due to the wind (which may or may not be applicable depending on what you have in mind), the physics of the instability leading to fluttering has been worked out in a fairly celebrated paper of 2005 by Argentina and Mahadevan. They argue that:

[...] in a particular limit corresponding to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode.

I suspect this paper and probably some of the papers that cite it would be the right place to look. As you can see, this part of the question that you've asked is of fairly high interest in current research.

Second, how does this motion generate sound? This is also an interesting question but I know less about this. I would suppose that some resonant vibrational modes of the sheet of paper that you're asking about (those involved in the flapping modes described by Argentina and Mahadevan) generate the sound. But I don't know very much about sound generation or acoustics.

It is always about a resonance between the vibrating element and a pressure mod in some resonator (in case of sharp edge, the edge itself oscillates).
I believe the oscillations itself are produced by the turbulent vortices forming Kármán street behind the reed or edge.

EDIT: I have even found a reference: http://arxiv.org/abs/physics/0008053v1

EDIT2: In detail, the process starts with static edge in laminar flow; speed of flow increases and finally the Reynolds number exceeds critical value in which streamlines start to disengage from edge first forming vortices in Karman street (this is called Strouhal instability) and then a totally random turbulent flow. The vortices interact with the edge "poking" it quite randomly (Karman street has some frequency, but I think it does matter only for some narrow cases); now the process is driven by resonances. The edge has some resonance frequencies, the air around can also have them if enclosed in some container, in case of some instruments the musician's lips are also involved -- all those for some kind of mechanical filter that amplifies certain frequencies (instruments) or ranges of frequencies (random setups). Finally, those mechanic vibrations induce pressure weaves in air that we hear as a sound, again either clear as in case of instruments or a noise as in case of trees, roofs and other stuff.