All my attempts to "clean and repair" a sticky-seasoning layer have ended badly as well. I know who already snickers in the background, but my opinion is: start clean. Give the pan a lye bath and a good scrub, then reseason with a better seasoning.
"The new hotness" of flaxseed oil goes back to the fact that it doesn't go rancid easily, without heat it just dries out making a film which can protect things like wood. I bought into it, and seasoned a pan with it, and wondered why all my seasoning tries were unsucessful (I stripped and reseasoned 3 times, I think). I came to blame it on the smooth forged iron.
Then I got Cookwise and read the chapter on fats. And surprise, what does it say? That PUFA stick to everything around. (Makes sense, if you stop to think about it - those unsaturated bonds are unstable, they itch to break apart). So, when I got my next iron pan, I seasoned it with three (very thin) layers of flaxseed oil (for a solid base which will stick to the pan and the finishing layer) and then two layers of lard. After the oven, I heated it from brown to almost-black on the stove (empty).
This seasoning turned out perfect. I made crepes on it, re-oiling once every 7-8 crepes only (no fat in the batter). The pan released them like a charm. The old flaxseed-seasoned pan still sits around with some carbonized matter burnt onto the seasoning, and waits for a lye-flaxseed-lard session.
Of course, I would still take some caution with new seasoning and oil well the first few applications (I only tried the crepes after I noticed that less problematic items work great). And if you tend to often fry with the fashinably-healthy nonsaturated vegetable oils, don't heat them too much, else they could bake in a sticky-seasoning layer onto the pan. In the worst case, if you do get sticky-oil (but not carbon) buildup, try adding a new lard layer before you strip-and-reseason.
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
Do you need to remove a bunch of burnt-on stuff as well as the season? If the pan is clean but not rust-resistant or non-stick like you want, I'd suggest just treating it like you were doing it for the first time and just season over the old. It's not like you care about hurting the old season--you'll just be thickening it and filling in gaps.
If you need to get it back to day zero, there are definitely questions here with good answers about how to do it.
But the first thing I'd try, since the day zero cleaning methods are fairly drastic, is to make sure it's as clean as you can manage, then just go ahead and season. I have had good luck rehabilitating pans that were poorly seasoned but otherwise OK by doing this.
Based on your response in the comments, I would definitely heat up the pan in the oven as high as it will go, and let it go until it stops smoking (put the cold pan in the cold oven to start). That should burn off/dry any excess oil, which it sounds like you have. Then I'd let it cool enough to handle, then season as if it were new. I don't care for the "tacky" seasoning because it's too easy to get a buildup of unseasoned grease. So I'd cook that down/off and start over. And I always rinse with the hottest water my sink makes, to prevent buildup--no soap, though.