Nobody will ask for your visa at Heathrow unless you have booked your flights on separate tickets and therefore need to check in at Heathrow.
If you do have to check in at Heathrow, you should show your South African passport to the airline when you check in, because your South African passport entitles you to travel to Kenya without a visa.
When you arrive at Heathrow, before you can check in for your second flight, you will have to clear UK immigration. Here, you will show your Dutch passport, because you don't have a visa in your South African passport. This is probably why you were warned not to show your South African passport. (Other reasons to show the Dutch passport include the much easier and shorter immigration process for EU citizens.)
If you are in doubt at any point in the process, there is no harm in showing both of your passports to the same person.