How can I fix the "incompatible data" issue when flashing Cyanogenmod onto my Xperia Z3 Compact?
Usually just wiping /data from the recovery and/or installing the package again immediately after first failure should get you through.

However if it doesn't, then you might want to ditch Cyanogen Recovery (that comes with the boot.img you flashed) and use TWRP. Find some here at XDA-Developers - basically any one that integrates TWRP should work, because you will be substituting it with CM's boot.img later when flashing, but it's advised that you choose one that's built for the same Android version you were on before flashing.

This sounds a bit hard to swallow and it is, but it's essential flashing skills and you will need it. With TWRP you can also put the package in internal storage and flash it from there, instead of relying on your PC to do a sideload.