I tried seasoning an aluminium kawali and was pretty successful doing this.
I cleaned it very well and then layered it with a bit of oil (use peanut or canola) and then baked it outside on the bbq (or oven) for 30mins each time and then reapplying oil when it’s cooled down to touch. Important and ensure your kawali is upside down when baking and remove any handles.
I repeated these steps 5 times ( see pics attached for result).
Before using the wok properly, I sacrificed onions and ginger and burnt it for seasoning and then did the same thing with chicken pieces.
To clean I used warm water, wipe it paper towel and dry it on stove top to fully dry the kawali. I then, apply some oil on it before storing on paper bag until next use.
Check the bottom of the pan; often useful information is stamped there. Like the brand, sometimes even model number. Assuming nothing useful:
Steel and iron are ferromagnetic. That is to say, a magnet will stick to them. Both are unlikely to be Teflon-coated (edit: though Wikipedia informs me they exist). The black (which is hopefully somewhat shiny) is seasoning (cooked on oil). Iron would probably mean cast iron, and would generally be heavy (my cast iron wok weighs in at well over 10lbs). So, if they magnet sticks, you probably have steel.
Some stainless steels are ferromagnetic, but most aren't. Stainless is also unlikely to Teflon-coated. But it'll probably be shiny, at least on the outside. So, if not magnetic, its probably aluminum. Aluminum is probably coated.
Teflon isn't the only coating that may be used. It could be anodized aluminum as well (which, I guess, may not technically be a coating). Or one of the newer nonstick coatings. They all look different: Teflon is very dark gray to black, anodized is light gray to dark gray. The newer ones unfortunately are numerous and some can be any color. (Your description of the color sounds like Teflon to me).
You could also try cooking a scrambled egg in it; start it in a cold pan. Teflon in at all good shape will release the egg very easily. Seasoning will, unless very good, probably have you cursing.
Best Answer
The way it is flaking off (flakes sticking out instead of breaking off) suggests it is an old-school (non reinforced) teflon coating, not an enamel.
If the underlying metal is actually stainless (not likely to be carbon, would not look bright after that abuse) steel, you could make it usable, but it is unlikely to be worth the effort - the remaining coating won't come off as easily as you think. If it is aluminium, forget it - bare aluminium cookware is controversial from a food safety/health perspective, especially if the unknown alloy used wasn't chosen with intent to be a cooking surface.
As it is, it is unusable as a nonstick wok - which is best for some stewed/braised dishes - but you want an intact coating for that.
It is unusable as an uncoated wok, where the last thing you want is any nonstick coating that can only take limited heat - even if intact that is. Some modern nonstick types that are rated to 350 or 400 °C (not °F!) could be ok for a saute/stir fry wok - old school soft teflon isn't.
The example shown would, at best, serve as a driver for bamboo steamers.