Yes, the previous option was available by selecting: Commands > Flex Skinning > Export Flex Skin
This essentially exported the selection as an optmized PNG. Looks like the command above will accomplish the same thing, it's really just a shame that Adobe removed something that was so helpful and native to the application.
I'm just not familiar with Flex, so I don't know why it's been deprecated, etc.
Have you tried copying the Flex Skinning folder (in the application's Configuration > Commands folder) from CS5 to CS6? Maybe it'll still work.
Incidentally, I tried the above, and it seems to work! However, using Export... > Layers to Files might be a more standard (or native) approach, as described in this article:
Let me know if this works for you. Also, I'm curious to know more about why Flex Skinning is no longer a feature.