In version CS5 when copying a file vector / group / transparent image and was pasted into Flash, it was structured in the Library, and without many complications, still bore the effects of color and shadow. In CS6 it is no longer available?
The following Flash forum posting may help answer your question:
The "correct" answer suggests saving the Fireworks file as a PSD and then importing that PSD into Flash. I'm not very familiar with this workflow. You might also try exporting the Fireworks file in the FXG format (File > Export..., then choose "FXG and Images"), then importing the FXG file into your Flash library.
Hope this helps!
P.S. Do you still have CS5? If so, you could copy-and-paste directly into Flash CS5, and then from Flash CS5 to CS6.
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