Ok, well I found a few pics, one is a screenshot and another a poster. The screenshot changes a few things since now it looks like the stem is curved.
The image from the poster looks like the pipe pictured above in this thread.
No doubt they used multiple pipes in the movie. I just purchased this pipe...
off the web. This is the same brand, Savinelli featherweight, just a different model. It looks like it has the same slits from the Warner Bros. pic. I've sent out a few emails to some of the larger pipe shops on the web asking if they still have any of the discountinued featherweights, but no word back yet. In relation to Robert Downey Jrs. hand, I have no doubt that the pipe is some sort of featherweight pipe, just not sure if it's the Savinelli at this point.
And of course, there is a high percentage chance that this is a custom made pipe, like a few people have posted here.