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.
apt-get -d install backtrack-ati
This will download the packages in apt cache. So you have to install the packages ignoring dependency with ati-driver (the broken package).
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 of course break dependency, so you can't do apt-get upgrade anymore; but that's another story.

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).
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

Connecting to storage... connected

The following cores seem available...
#1: 'CPU-Core (SSE2)'
#2: 'CPU-Core (SSE2)'
I missed some additional important configuration step for pyrit, or the trick simply doesn't work?