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.
You may notice the black residue if you fry eggs in the pan as well.
Most likely, the black residue is charred (greasy) food sticking to the seasoned oil. Since Flaxseed oil has low heat tolerance, it could be that disintegrating, too. Otherwise it could be related to the iron in the cast iron which isn't bad for you (some say even good).
a) Is it normal: Yes if you keep with the same regiment (recommend you don't).
b) What is Wrong: Water won't perfectly wash non-polar chemicals such as burnt solids in grease (milk solids while making ghee), so the hot water no-soap routine leaves the stuff in pan.
c) How can I fix it: Try the following going forward:
After you finished cooking and while the pan is somewhat hot, put a heap of salt in the middle and with a paper-towel spread and lightly scrub the pan. The salt will pick up the would-be black stuff, largely disinfect the pan, and the abrasive properties of the salt helps with the cleaning.
Wipe off the now brown salt from the pan and rub-in the coat of oil as you normally do. The new coat will stick better to through the salt's abrasive effect.
This routine won't eliminate residue altogether. But it seems to work great long term.
Note on oils:
Flaxseed oil is best consumed cold and within three weeks. I haven't heard of a credible source promoting seasoning the pan with flaxseed oil as it has one of the lowest smoke points in the oils. Use a more heat tolerant oil like light (not extra-virgin) olive oil or canola.
Best Answer
AFAIK you need to heat the pan to let the oil oxidize and polymerize¹ so that it will form a chemically protective and non-sticking coating.
If you wash your cookware with soap you will have to do it every time. For that reason some people don't wash cast iron at all and wipe it with a clean cloth or paper towel after using. (Burned oil is apparently not very tasty to bacteria and fungi so your pan stays relatively clean and bug-free.)
From my personal experience, meat sticks to untreated cast iron like glue, but on a well-maintained thick iron pan it glides like on Teflon.
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¹ I don't know if it makes any chemical sense because all references to polymerized fats I could google up were in relation to reoiling (seasoning).