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.
It looks like your pan needs a hard cleaning and a re-seasoning. I run into this about once every 2-3 months (depending on how much I use it).
My tried and true method is to break some rules at this quarterly cleaning. I'll scrub with an abrasive scotch-brite, SOS Pads or similar scrubbing pad. During this time I often use about a quarter cub of baking soda, and towards the end I'll even use a little bit of dawn dish soap to make sure I've removed all of the particles, which amount to fine iron filings.
I've even resorted to very high grit sand paper to even out some areas in very serious issues on my handle. Now it's important to rinse and dry the pan COMPLETELY.
I then carefully rub crisco (less smokey than lard) all over EVERY surface of the now shiny and smooth pan.
Then, invert pan in oven over a baking sheet or foil to catch any mess, and bake the pan at 500F for roughly an hour or two, or until it is uniformly black.
If you have access to a clean, wood burning put, that's what my grandmother swore by, but I find the 500F oven more consistent.
I am not certain if this would work for your high carbon steel pan pictured in the first photo though. I would read up on that.
Best Answer
I have the same pan. Are you following the instructions that come with it?
The center is too burned.
Flaky is not good.
The border is not seasoned.
The border is not rusty.
Is your fire big enough for the pan?
You should clean the pan (thorough scrub with salt) and re-season. See this Q&A