There are a dozen flights a day between Mombasa and Nairobi as they are scheduled domestic flights you only need to be at the airport about an hour before (many people arrive later than that). There is generally not much of a queue at check-in, unless a package holiday company or an NGO / Charity has a party booked on your flight, then it depends how many people are in their party how big the queue is. Also if one of the big holiday charter flights is due to depart there can be a big queue at security to get into the airport, but most of the time there are just a few people going through. On the way to the airport you cross onto Mombasa island then across a causeway. this causeway is the only road from Mombasa going inland towards Nairobi, so it is a traffic bottleneck and it is also a steady incline so there are always slow moving trucks on it, which frequently breakdown so hold ups are common, I always allow an extra hour when going to the airport in case of hold ups on the causeway.
I presume you are referring to a Thomson safari package, so no doubt you will be taken to the airport well in advance, because package companies always seem to do this. Hopefully someone who has been on the same package will be able to tell you their experience. Are you flying from Mombasa to Nairobi to go on safari, or to catch a connection home?
If you do get to the airport very early there is a terrace cafe on your right before you enter the terminal, I usually stop and have a drink or two there before going through into the terminal. The Domestic departure area is reasonably pleasant, there is a cafe, tables and chairs and the standard airport seat a shop and a few tvs mounted on the walls