Nbo - Mba Transfer
From Amsterdam your parents will have their bags tagged through to Mombasa, as well as have their boarding cards issued (try and ask them to get a seat on the right hand side of the aircraft, as on the morning flights they get a fantastic view of Mt. Kilimanjaro).
On arrival in Nairobi, they clear immigration, collect their bags and then clear customs. When they exit customs, turn left, and walk through the car park to terminal 3, where they go through a light security check, and hand in their bags for the Mombasa flight.
Then it is one more security check, and a wait on a plastic seats. Nairobi airport is not great, especially domestic terminal, and there is no lounge. There is a coffee shop which serves good coffee, cold drinks and snacks.
Mombasa airport is not that much better either.
But they will enjoy Momabsa. I got back from there yesterday, the weather is warm, a bit of rain, but sunshine too.