A one hour transfer should be OK (I've successfully made one hour connections in NBO several times this year). As has been mentioned, NBO is relatively small and the FAs should announce the gate numbers for connecting flights while you're taxi-ing in on arrival.
Your biggest risk is probably a delay in KQ117 leaving AMS - as it'll be winter in Europe, weather-related delays are not uncommon. However, even if you're up to about 20 minutes late into NBO you should still make the connection; if it's tight, the KQ ground staff should meet you when you dis-embark to rush you to the next gate (if you're travelling in eco, try to get a seat near the front of the AMS-NBO flight, so you're off quickly). Even if you miss your scheduled flight to JRO, the good news is that there's another one at 10:45.
However, note that asking about your bags at the gate in NBO is not very reliable. In AMS, they have a live-updated system, so they can directly check whether or not your bags have actually been loaded onto the plane. However, in NBO the system doesn't have live updates, so although they can check whether your tag-numbers are associated with your reservation (and whether your bag was loaded in AMS), they can't actually check whether your bag has been loaded onto the JRO flight. If you ask the ground handlers out on the tarmac by the PW flight (you'll have to walk across the apron to board it), they might be able to tell you whether your bags are on board.