Kenji Lopez-Alt (formerly of Serious Eats) believes flaxseed oil results in seasoning that will flake off. I've not heard that allegation from others, but I admit he generally does his homework.
I drank the flaxseed Kool-aid (courtesy of this article) when I first started purchasing cast iron ~6 years ago. The flaxseed seasoning is incredibly hard, which is great, until its brittleness causes it to flake off. I was constantly losing bits of seasoning nearly every time I used a pan. (my working theory is that thermal expansion/contraction causes parts of the polymerized coating to lose bond with the steel over time).
I finally got sick of dealing with it, going at all my pans with an angle grinder and flap disk to remove the old seasoning and started over using bog standard vegetable oil. I've not had a flaking problem since. I do need to re-season more frequently, but that is easy and quick to do.
ttps://www.goodhousekeeping.com/food-recipes/a32733/wire-grill-brush-dangers/
The article suggests alternatives such as coil brushes or crumpled aluminum foil instead. Also there are chemical methods.
Wire tools deserve considerable respect and should be used only with protective gloves and eyeware and even skin protection, since spun-off pieces of wire can embed in eyes or bare skin (and you may not notice). Good news: any embedded wire or steel fragment shows up like a lighthouse in an x-ray, making them extremely easy to locate.
Luckily, later on I learned a better way - a cooking spray called Baker’s Joy, which is essentially oil impregnated with a little flour. The flour seems to help speed up the seasoning process, so you can get to a well seasoned pan quickly. I usually heat the pan up, either in the oven or on the grill, then spray the Baker’s Joy when it’s still very hot. I make sure the pan is well coated, then I wipe out the excess.
This technique won’t give you a hard shell like the flaxseed oil method does, but it does seem to produce the same results as multiple seasoning sessions in a single pass. I’ve also found that cooking an onion in the pan helps when the seasoning isn’t quite what you want it to be yet. I read once that it’s a traditional method for breaking in a carbon steel wok.
Cook’s illustrated did a short piece on the method not long after it came out too, and found it satisfactory, at least with a minor tweak or two,