Whether to take or not take a cleaning kit boils down to:
length of trip,
number of animals one plans on hunting,
weather conditions you are hunting in,
terrain - soil type - in the area you are hunting,
check baggage weight limits,
My first trip to the East Cape, RSA was for 7 days, hunted 6 animals, my second trip to the East Cape, RSA was for 10 days, hunted 7 animals, on neither of these short trips I didn't bother with a rifle cleaning kit.
My third trip was 28 days, 14 days in Zimbabwe and 14 days in the East Cape, for a total of 9 animals. My fourth trip was for 42 days, 4 different outfitters, 3 different provinces in RSA, hunted 38 animals.
I packed a gun cleaning kit containing:
2 - 4 ounce spray bottles (travel bottles from Walmart), 1 with gun oil and 1 with fouling removal solvent,
some patches,
cotton swaps - Q-tips
1 each caliper specific: brass bore jag, bore brush, and bore swab
4 pc brass cleaning rod
2 cleaning rags - old wash clothes
Except for the cleaning rods, everything else is placed into 2 baggies and packed inside the firearms case.
Due to the length and amount of shooting I was doing I cleaned my firearms as needed on these longer trips.
As long as you stay within the airlines liquid limits you shouldn't have any problems.