O.k. I'll do my best, I'm not a registered, tech, but I've been in the industry for a few years now. I agree w/ the vet. Probably allergy is the root of the problem, but sounds like a staph infection secondary to the allergies. Did they try steriods short term, or an injection? Sometimes if they can take the itch out for a while, they can calm the skin down enough to start healing, although you said he doesn't seem especially itchy, just flaky and stinky - the smell is your key, definately a sighn of no good. I'll bet they give him a round of antibiotics.
As far as food, have you tried any hypoallergenic stuff, like rice and venison, i.e. change the protien source? You usually need to take about a week switching (while combining the two) and then up to 8 weeks to see if chng makes a difference. Then if you switch back and problems arise, you know it was food and not environment.
Allergies in dogs usually come w/ itchy ears (can lead to ear infections secondary to allergies, so keep those ears clean w/ otomax or equivalent, ask the vet), and licking feet, in addition to general scratching.
Scratch testing is expensive, and sometimes it just turns out that the dog is allergic to everything, like people... grass, trees, carpet fibers, dust, you name it. Then you go through the desensitization process w/ shots. (Also expensive and may or may not be very effective, some do well, some it doesn't help much). This usually entails the vet administering the injections whenever dosage is changed (to respond to possible anaphalactic - sp- shock) - which adds to the expense of the shots.
Most of the over the counter shampoos like you buy in the grocery store, are crap (same for the flea products). Speaking of fleas, could be allergic to fleas and develop staph 2ndary to that reaction. One flea can be a real killer to a dog that's allergic, invest in some Advantage, or if near tick territory, Frontline is your best bet. Also, advantage will wash off w/ baths, and you are probably bathing frequently because of the smell - could also irritate her. I like the oatmeal conditioner by EpiSooth, a very popular manufacturer makes Sebolux medicated shampoo (also from your vet) for mild seborrhea. These products were sold by all 3 vet offices I worked in.
For coat conditioners, I like DermCaps brand. You can get a liquid which you pump onto their food, or capsules (looks like vitamin e caps). I find the liquid the easiest. It contains concentrated fatty acids, and should help the flaking.
Well, sorry to be so windy, hope this helps. But bottom line, since it's gotten worse lately and because of the smell, I'd get him/her in to see the vet so they can get her some immediate relief.
Hope this helped, pm me and let me know the update.