I have up to Pandaria for most professions. Looking to fill in from that point:
Done on TWW and Midnight.
Draenor: For primary professions & cooking kill mobs until you get the quest to unlock the profession (and matching garrison building ex. Cooking) . For mining/herbing/skinning - gather until the unlock drops. Fishing - visit the trainer in Ashran.
Legion: Mining/skinning/herbing initial unlock & follow up quests from gathering. Fishing - trainer. Cooking - kill a rare that drops a recipe as per this Wowhead Guide. Nomi will pop-up & after a few quests will send you to find 5 more recipes. Then welcome to the grind of daily quests. Other professions, visit the trainer and follow the quest chain. Each recipe has 3 levels, locked behind quests, vendors (rank 2) or mobs.
BfA - visit the trainers around Boralus/Zandalar then follow the quest chains.
DF - you get the KP from doing quests from the trainer in Valdrakken and some knowledge stones that drop from dirt piles/treasures - there’s a starter quest where you enter the Dragon Isles for a chain to unlock these. Sparks drop from a quest Jump-Start? Jump-Starting! around the back of Valdrakken (main city). There’s also a set of one-off KP from various NPCs around the Isles. I suggest following a guide like this one on Wowhead for Tailoring.
Check out wow-professions.com
It has a straightforward step by step guide for every profession for every expansion
Good news for BFA: Has nifty craftspeed enchant.
Bad news: Lots of rep gated item recipies for Rank 2, even cooking. Then rando world quests to get rank 3.
PvP patterns need handfuls of honor tokens to rank 2 and 3.
But they do bridge the last few skill-gap levels for speed leveling.
Nazjatar Faction PvP vender should have more, for more tokens. As well as some extra normal profession patterns the normal BFA prof trainers lack.
And the reclaim/recycle system helps minimize materials needed/lost at least. 
Allow alchemists to reclaim old and depreciated potions and elixirs to create and level our profession.