The FGLRX installation requires the removal wine1.6, is installed from the official repositories for Ubuntu 14.04. Tested on the deb-packages from the website and install through *.run --buildpkg.
fglrx-core not compatible with ocl-icd-libopencl1, which is in the wine dependencies.
What makes you think it would be compatible? Fglx-core is OpenCL 2.0 and most likely wine hard depends upon ocl-icd-libopencl1. I'd wait for official Ubuntu packages from the distro rebuilding Wine against fglx-core.
Debian doesn't have the latest Omega Driver for obvious reasons. The 14.12 driver is still on Debian's watch list.