I wouldn't try transferring mod data, since file organization is a little different; as wookiejedi said, it's super easy to install all that from Knossos.
As for transferring campaigns, I think you can just copy the .csg files from wherever they live in non-Knossos FSO to %AppData%\Roaming\HardLightProductions\FreeSpaceOpen\data\players\ once you've installed the Knossos versions of everything. You can try to copy the .plr files from old-FSO as well to keep all your old pilot settings, but if that doesn't work try making new pilot profiles from scratch, but make sure the new names exactly match those of your old .csg files.
FWIW, I've used the above technique to recover campaign progress when a pilot profile got corrupted, but I've never tried it between different installs of FSO, let alone between Knossos and not-Knossos.