I have an old Kona mtb with front suspension fork that is completely shot, front wheel haven't got much life left in it either.

The frame is built for a 410mm a-c P2 559/26'' fork. However, I have a new, excellent 622/28'' dynamo front wheel that I would like to use and found a 700c CX fork with 405mm a-c (Kinesis Crosslight 3 Alloy Fork - Kinesis Bikes). I cannot figure out why this would not work but thought I better check if there is something I am not thinking about.

Are the rake/offset numbers the same?

Ahh.. no, original fork was 39 mm vs 700c fork has 45mm

Head angle is 71

Do both have a 1-1/8th steerer tube? Straight?

Yup, both 1-1/8 straight.

Well the 700c (622) rim will have a 31.5 mm greater radius than the 26" (559) rim so the bike will "stand" that much higher in front, all else being equal. That will noticeably decrease the head tube angle and increase the trail. However, depending on what tires were used on the 26" and what you use on the 700c, that difference may be less, more or the same. The 5 mm difference in a-c dimension is about negligible but the tire size and rim dimensions are not.

true, it will be about 30 mm difference in diameter so about 15 mm higher stance based on wheel size. Maybe go for e.g. 395 mm a-c to compensate? Would that work? Much more options with 395 a-c in CX forks.

A 58-559 tire is has a LARGER OD than a 25-622....... Generally 559 tires are wider than 622 tires, and thus the overall diameter difference is a LOT less than the rim diameter difference.

I sort of assumed the OP was not going to fit a 700-23 or 25 mm tire but something more in keeping with the mtb wheel he is replacing.

If you already have the wheel and fork in hand, just slap them on and try them out. Even if you don't have a tire yet, just roll around carefully in front of your house to see if you like how it feels to roll on it.