The best is flax oil. The next best is soybean oil. The third best is liquid canola (not hydrogenated Crisco).
This is because of where those oils are listed on iodine index; which is a measure of how much an oil will polymerize. Polymerization is when oil turns into plastic and is the actual chemical process responsible for "seasoning".
Here's a whole site dedicated to this topic with more detail:
Chemistry of Cast Iron Seasoning: A Science-Based How-To
I can't speak authoritatively, but I do have all three types and have had good luck with my seasonings, so I'll share what I do.
For cast iron, I use solid vegetable fat exclusively (Crisco). I did the original seasoning by coating it in fat and baking in the oven. To clean it, I use salt, Crisco and a paper towel to get any food bits off. I then get the pan hot and wipe it down with a little more Crisco. It's not PTFE nonstick, but pretty good.
For my forged iron DeBuyer fry pan, I followed the manufacturer's recommendation for initial seasoning: put enough oil in the pan (I use canola) to coat the bottom. Heat to smoking. I swirled the hot oil around to coat the sides a bit. Let it cool, pour and wipe out the oil.
The thing I've found is it takes quite a bit of use to develop the seasoning. Here's a picture after about a month's use - note how dark the sides are getting (the bottom is less dark because I learned a green scrubby pad (Scotch-Brite) will remove the seasoning entirely. Oops!).
I did some scrambled eggs for the sake of science, without adding any extra oil to the pan. They behaved as nicely as any PTFE coated pan I've ever used.
Today the entire bottom of the pan is that rich mahogany color, and a fried egg slides around in it like one of those goofy AS SEEN ON TV ads.
EDIT: Used the pan for over easy eggs this morning and snapped a new picture. This is about 3 months after the last photo.
Normally I can just wipe it out with a paper towel. If I've been cooking bacon or something that left residue, I'll run water into the pan while it's still ripping hot, then wipe it out gently with a sponge.
After that I heat the pan up and add just a tiny bit of canola oil. I wipe the oil around with a paper towel and put the pan away.
For carbon steel--like my wok--I treat it exactly the same as the DeBuyer pan. Clean gently, after each use get the pan ripping hot and wipe it down with some oil.
Best Answer
No, this isn't normal. A little flaking, perhaps, when you go over 600°F, but 500°F shouldn't do anything. It shouldn't even smoke.
Something is wrong with the seasoning on your pan. From the fact that its smoking, I'd guess its not sufficiently baked on. Alternatively, maybe the pan wasn't clean when you applied it.
If its just not baked on, I'd remove all the flaking bits (with some harsh scrubbing, sand paper even), clean it thoroughly, then bring it to around 300°F (stovetop or oven). This will make sure it is completely dry. Spread a thin layer of high-iodine value oil (flax seed is great, soy is pretty good and cheap and easy to find: look for the bottle that just says vegetable oil and check the ingredients, it's probably soy). Spreading is easy with a paper towel.
Next, toss into a very hot oven, 400–500, smoking is expected. Bake for 90 minutes, then turn the oven off. Allow pan to cool with oven. Once its cool, touch it. If its at all tacky, put it back in the oven, and bake for another hour (once again, allowing to cool with oven). It should be a shiny black at this point, and not at all tacky.
You can repeat the process to add more layers. Two should be reasonably non-stick to start cooking on.
If it still peels off after this, you're probably going to need to strip the seasoning and re-season the pan, after stripping it to bare metal. See What's the best way to season a cast iron skillet? to season it from bare metal.