I've got a pair of fairy wings I've created in Blender, and exported as FBX.  They're rigged with bones to allow for animations like flapping, etc.  When I load them into 3DXchange, they appear as per below:

However, I've noticed a few odd things:
- When I click the 'singularize pivots' button, the whole model disappears
- When I export the model to iClone 7, it doesn't appear at all
- The opacity and bump (normal map?) textures don't seem to have any effect

Furthermore, I'd like to set this up as an accessory in Character Creator, so that I can attach it to the various character models.  Yet 3DXchange only seems to show an option to create an iClone prop.  Any assistance on this would be appreciated.

I'm guessing here because I'm not a Blender user, but I believe Blender's units are meters and iClone's are centimeters, so it may be that your wings come in very small (1% of the size). Turning the grid on (Ctrl-G) will give you an idea.

It could be that Singularize Pivots moves the wings out of view. You can bring them back in view by clicking the Home button (the little house).

An accessory is simple a prop that is attached to a character.

So after exporting the wings to iClone, attach them to a character, position them to where you want them, and then save the wings. They will now be saved as accessory. 

To do that, navigate to the Accessory folder under Avatar Custom, select the wings, and click the "+" button.

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I'd already exported them with a scale of 100, as I'd run into that problem before.  As for singularising pivots, clicking the home button afterwards doesn't seem to do anything.  I'll have an empty selection box where the wings were, and that's it.  Pressing the home button and scrolling around doesn't show any sign of them.

Well, this requires a Blender expert. There are a couple of them here. I assume the textures are OK?

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I think the textures are okay.  I've tried exporting both with and without the textures, and got the same results each time.

Further to this, I've tried doing a test where I've just generated a cube in Blender, exported to FBX.  When imported into 3DXchange, it becomes a flat, 2D-plane when the 'Singularize Pivots' button is clicked.  If I import it from 3DXchange to iClone without changing anything, it appears in iClone as a flat plane.