As of the time of writing this article, Flux Mining has been removed and is pending a future rewrite; as such, this will serve as a historical explanation.
This sub-skill had two iterations in the past. When it was first added, it was a passive that had multiple ranks which could be advanced by levelling up the mining skill. It was later changed at some point in 2016/2015 to be bound to an item, and then reverted back to being a passive for a brief moment in early 2019.
When the sub-skill was a passive effect, it could occur regardless of what pickaxe you used as long as it did not have silk touch as this enchant nullified the effect. However, when it was an item, you were required to smelt a pickaxe within a furnace - this converted the pickaxe into a Flux Pickaxe that you could use to mine, and trigger the effect with.
Unfortunately, applying enchants to the Flux Pickaxe would nullify the effect rendering this iteration of the skill quite useless to players who had access to end-game enchantments. Many players would opt for their main pickaxe and never use the Flux one.
In both iterations, the effect was the same - it had a chance to instantly smelt gold or iron into an ingot as soon as you mined the ore.