Wow, Jim. You have a LOT of opinions and suggestions here, so I am hesitant to even throw another one in the pot. As a building contractor, I have put down a wood floor or two over the years. Most of those were glue down or nail / staple down applications. However, in your case, I would suggest neither.
First of all, congratulations on your decision to build an earth sheltered house! That alone should greatly reduce your heating and cooling costs.
I would NOT pour the kitchen slab separately from the rest of the house slab if you can pour it at once and still have the recess that your floor requires. That would only promote cracks around the edge and a place for moisture and termites to come up. Keep the slab continuous and also the plastic vapor barrier under the slab. That is especially important around wood floors. You need a dry slab under there.
I question the amount of benefit that in-floor radiant heating system would have under at least 3/4" of oak flooring in an already underground or earth protected home. Is it really needed in the kitchen area? How large is your kitchen and how open of a floor plan do you have? Perhaps something as simple as a ceiling fan might help air flow and distribute heat from the other rooms where there is in-floor heating? The cold feet syndrome would definitely be more pronounced over concrete or tile than over wood. Perhaps it may not even be necessary if the kitchen is not too large? Also, would you normally have small rugs in areas where you would stand for a while, such as in front of the kitchen sink or countertop where food prep would occur? That would not only pad the floor for extended standing, but also keep the feet warm with or without radiant heating.
Regardless of whether or not you use radiant heat in the kitchen area, you still have to remember that kitchens and bathrooms share one trait... they are high moisture areas where water inevitably gets on the floor from time to time. So, expansion and contraction is a situation that you will have to face no matter what.
Those things taken into consideration, whether you use the radiant heat in the floor or not, my recommendation is the same. First, when pouring the concrete, make sure that you have a good continuous vapor barrier extending under the whole slab and pour the slab as a monolithic structure... in one piece. Recess the slab for the depth of your flooring (usually 3/4") plus about another 1/8" to 1/4" for one or two layers of rolled foam flooring underlayment.
Install your cabinets on top of plywood or shims. The flooring should NOT extend under them. Instead of nailing or glueing your flooring, I would suggest that you get router or shaper bits (depends on whether you are using a full shaper or just a router table to mold your flooring edges) that provide a snap-lock joint rather than a standard flat tongue and groove joint. That way, you can install your flooring as a floating floor instead of a glue down or nail down application. This will allow your flooring to expand and contract with the temperature and humidity / moisture fluctuations (like when water is splashed on the floor or you want to mop it) without binding and warping and such.
Of course, like the others said earlier, a quarter sawn profile that has a face width of about 2 1/4" to 2 1/2" (not counting the tongue) will be much more stable than a wide flat sawn board. After milling the floor with the snap-lock tongue, simply install the floor directly over one layer of foam wood flooring underlayment. You do not need to glue or nail anything, but leave a small gap of about 3/8" - 1/2" around the perimeter of your flooring to allow for expansion and contraction. Of course, you must have your flooring very dry (6-8%, the dryer the better) before installation. When you are finished, either buy or mill your own transition piece for covering the gap where the wood floor adjoins the stained concrete floor, and also install base and quarter round or shoe moulding around the edges of the room and under the edges of the cabinets to cover the edge gaps there as well.
Use a very good polyurethane sealer over the floor and that will help with the moisture as well.
A guy that used to work for me years ago also was a professional skater and ran multiple skating rinks. Once a year, they would refinish their floors with a product my friend called Roll-On. Basically, it was a tough epoxy. The beauty of the product was very little prep work other than a quick sanding and cleaning of the floors was necessary, it was super tough, very high gloss, and looked great. It did not hurt that the product was simply and quickly rolled onto the floor with big paint rollers and then settled down into any cracks and self leveled. He used the stuff to refinish his oak floors at home too. Looked great. Not overly expensive either. You can use standard floor polyurethane, which will look great also, but it will not provide the water and moisture resistance and toughness that Roll-On will. Their Ultra_Clear product will probably be your best bet. It is a step up from the regular Roll-On that is used on most quality skating rinks. The nice thing about using a Roll-On finish for your oak floors in a kitchen is that it is highly water resistant compared to other finishes and takes wear and abuse really well.
You can read a little bit about their products here:
http://www.roll-on.com/floor_coatings.htmHere is a list of distributors across the U.S.:
http://www.roll-on.com/distribu.htmFor what it is worth, I hope this helps you some...
