Interesting find. A few comments:
- This trip was done in the late 1980s. Road in Africa have improved significantly since then.
- The route map between Nairobi and Khartoum shows a straight line. I'm guessing they flew for political/logistical reasons. This region is mostly Sahara desert areas (or Ethiopian highlands if they went a bit further east) as well as politically sensitive. After that perhaps following the Nile and/or on the water e.g. Lake Nassar?
- Even for that period, 278 punctures is a huge amount. When I went in 2013, we encountered a lot of thorns. Tires were perhaps better (I had two flats, lower than average but even members in my group with most were less than 50)