I've been all under the front wheel wells and can tell that the undercoating material which is flaking off must have been applied at the factory before assembly, because the fasteners underneath the fender well are not coated, but appear to be installed over the undercoating material. Also, it is not sprayed all over everything, as after market or dealer-applied material would be. Not a drop of overspray on anything.
Underneath all of it is shiny black paint (the car itself is black). Not one bit of rust anywhere.
The floor of the car is completely coated with what appears to be the same material and it is not flaking anywhere under the floor area of the body; only in the front and rear fender wells.

 

Very lucky if it's as good as you say.
Pressure wash uder the arches and scrape off the underseal, if there's any loose or damaged paint then derust, prepare and paint with POR-15 or epoxy primer. Thn apply a modern anti stone chip underseal and a good (eg dintrol) underbody wax on top when it's dried.
Check the floor thoroughly as although it may seem intact there may some loose underseal trapping water leading to future problems. I would coat the whole underneath with a good underbody wax as well.
Put some cavity wax in the sills, behind the head lights etc in fact lots everywhere!!

 

Thanks for the info. Here in northern Louisiana there is no road salt and auto corrosion is minimal, but we get a lot of rainfall and humidity is generally pretty high: I read British hobbyist magazines and I know you all would love to see some of the rust-free cars we have in salvage yards: Jaguars, Volvos, the occasional Porsche, BMWs, Mercedes-Benz.
Anyway, I am with you on your advice, some of the products are hard to get here in the USA: Dinatrol, for example, has a black wax which I would use and it seems like it is about what is flaking off the car now, as wax has a reputation for eventually drying out and turning loose (after all, the car is 27 years old, though). Do you know Mike Sander's grease? I can't get it, but I bought some materials and I am trying to duplicate it for the cavities of a 1951 Buick I am cleaning up. I suspect it is similar to if not exactly the old NATO mil-spec rust preventative which is 90% technical petrolatum and 10% beeswax, heated to 250 C and sprayed.
I am keeping the car as dry as practical until I can get the windshield and rear glass out to inspect the channels.
Regards!

 

Somewhere on here are formulas for making a material similar to Waxoyl.

Fluid Film is easy to get in the US.

 

From the sound of it, I thought Mike Sanders formula was more like a grease than a wax.

 

I have seen several do-it-yourself formulae for underbody wax: variations of beeswax and /or paraffin mixed with some motor oil, and dissolved in white mineral spirits to a sprayable consistency. No doubt it will work fine. I plan to mix up a batch soon.
Mike Sander's material is a grease: since I found an old NATO specification for anticorrosion material, consisting of petrolatum (think of the base for Vaseline: that's a more refined form of petrolatum) mixed with 10% beeswax, heated to 250F, and sprayed onto and into whatever needs protection, I think this is about it. The two benefits are: it will continue to flow into crevices and pinch welds, and it won't dry out like the waxes tend to do.
I have a 5 gallon pail of white petrolatum (it's beautiful), and 5 pounds of beeswax. I plan to mix up a batch and try it on a '51 Buick I'm working on. I already have a spray gun with a cavity wand. Hey: embalming fluid for old car bodies!