This depends on two things: the file size of the images from your cameras (jpeg and raw files differ vastly), and the number of images you anticipate taking. While the latter can vary substantially, the likely range is from 2,000 images for the entire safari, to well over 2000 per day for many people. We have had many photographers take 50,000 images on a 10-12 day safari.
We recommend that guests shooting jpegs with consumer point-and-shoot cameras take at least two 32GB cards to cover their needs (we usually have extra cards to loan out if needed). And bring a high capacity flash (thumb) drive for storage.
If you are shooting Raw files with a large megapixel/high speed cameras, your total memory needs can add up quick — from 500GB to +2TB — depending on the length of the safari and how aggressively you shoot. Shooting any video from your DSLR will double or triple the memory needs. If you fall into this category of high memory use, several high-speed 64-256GB memory cards and a couple 2TB drives or even two 4TB drives may be needed. Keep in mind that when shooting high volumes downloading speed becomes an issue and the faster the storage drive, memory cards, card reader and computer ports, the better.
We usually have extra memory cards (CF, SD, CFast) to loan if you run short.