How to make my AMD GPU work with the Flatpak version of darktable?

You have this in your logs, so the driver works but can not compile the opencl code.

0.5255 [opencl_build_program] could not build program: CL_BUILD_PROGRAM_FAILURE
     0.5255 [dt_opencl_device_init] failed to compile program `demosaic_ppg.cl'!
[opencl_init] no suitable devices found.

There is something missing inthe fedora packaging: the rocm package is missing some llvm binaries.

This has already been mentioned in the following thread: OpenCL on Fedora 40 with ROCm (AMD) not working - #25 by m-a

I had a similar problem on my standard fedora install (not atomic) and I think I had to install clang18 manually.