It's a known problem. AmiCygnix uses 16-bit screenmodes, but expects a big-endian 16-bit mode. However, Southern Islands GPUs (like the R7 250X) don't support big-endian 16-bit textures. So, 16-bit modes are little-endian. Since AmiCygnix assumes that it has a big-endian mode all the colours are wrong.
AFAIK the Amicygnix author has been informed, so hopefully we'll see an update that addresses this problem.
Hans
I have here a fixed version of Amicygnix. That works well with my RadeonHD7850 .
It is still beta, nothing for release.