Firstly, I think that what someone would regard as 'essentials' depends upon where you are coming from.
I come from the UK and in my opinion, there is very little that I can't get here in Kenya, but sometimes at a high price!
Food; (bearing in mind that I live outside Nairobi) Its difficult to find items such as smoked salmon, Marmite, fresh cream, semi skimmed milk, strong white flour. Iam aware that such items are available, but you might have to hunt for them. UK breakfast cereals cost several times the UK prices, so I avoid them.
Vitamins;Â my wife takes and boy are they costly!
Soaps, shower gels, cosmetics; we can buy everything we use in Kenya. My wife likes MAC, which is available in Nairobi. We also like Dr Organic products, which are actually a bit cheaper in Kenya, than in the UK. If you like 'Body Shop' stuff, this isn't easy to find.
Electricals; TV, fridges, freezers, washing machines, cookers, food mixers, irons etc are all readily available in Kenya. Prices are about the same, or lower than in the UK. When we moved our household items in 2004, we brought all the electrical items with us. However we had a duty free container. I would recommend that (if one is self funding) the cost of shipping doesn't exceed the cost of just buying what you need here.  If you want things like the latest Apple products.....better bring them with you, as there is quite a lag on release dates in Kenya.
It is challenging to get a decent vacuum cleaner in Kenya. It's also quite difficult to find a decent ironing board, but they are available here and there.
Vehicles; its very costly to buy a vehicle in Kenya, so if yours is right hand drive and less than 8 years old, it's worth considering importing it. Duty may or may not apply, depending on status/reason for entry. However, for diesels, emissions equipment such as particulate filters cannot cope with the Kenyan conditions. Rare or unusual models can be difficult to service. Concerning vehicle spares, there are many fakes on the market, so importing these may be worth considering.
Bicycles: not easy to get a good quality cycle, in Kenya, particularly for children. Many suppliers seem to stock poor quality Chinese products that fall to pieces rather quickly.