For now I managed to install the atistream and cpyrit-stream packages with a trick. Manually install the driver from the official ATI site. Then download the needed packages.
This will download the packages in apt cache. So you have to install the packages ignoring dependency with ati-driver (the broken package).
apt-get -d install backtrack-ati
This of course break dependency, so you can't do apt-get upgrade anymore; but that's another story.
dpkg --ignore-depends=ati-driver -i /var/cache/apt/archives/atistream_1.4.0-bt2_i386.deb
dpkg --ignore-depends=ati-driver -i /var/cache/apt/archives/cpyrit-stream_0.2.2-bt2_i386.deb
This seems to work. I run Xorg with flgrx driver and dual head configuration, and have atistream and cpyrit-stream installed. I say "seems" because pyrit doesn't detect the GPU (I have a HD4570).
I missed some additional important configuration step for pyrit, or the trick simply doesn't work?
Pyrit 0.2.5-dev (C) 2008, 2009 Lukas Lueg pyrit - Project Hosting on Google Code
This code is distributed under the GNU General Public License v3
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#1: 'CPU-Core (SSE2)'
#2: 'CPU-Core (SSE2)'