Bringing a small compact rifle cleaning kit or a bore snake is a good idea for an African hunting safari.
Due to airline restrictions on fluids, especially flammable fluids, don't attempt to bring cleaning fluids. Your PH will have something you could use, if necessary.
You do not need to overdo rifle cleaning whilst on safari but it a good plan to give it the odd going over, especially if the rifle has been out in the rain.
Try not to over-oil the rifle as oil in the barrel, as you know, causes a different point of impact on the first shot. Also oil on the outside makes for more shine and acts as a magnet to dust.
Bring some insulation or duct tape to cover the end of the barrel to prevent dust and other debris getting in.
Always clean your own rifle on safari - never give your rifle to your PH or any other staff member to clean.