The Poisoner’s Kit tool offers a lot of opportunities for narrative interaction in D&D.

The mechanical implementation falls a bit flat. By the rules, the Poisoner’s Kit doesn’t do anything. The rules text gives you proficiency to create poisons. But, there’s no DCs for poison creation in the Player’s Handbook (PHB), Dungeon Master’s Guide (DMG), or the expanded tool rules in Xanathar’s Guide to Everything (XGE).

Poisoncraft

The DMG does speak on poisons:

Harvesting. If you’ve felled the right monster (there’s 4 listed), you can make a DC 20 Intelligence (Nature) check to harvest their poison. If you have the Poisoner’s Kit, you can use that instead, but you don’t get to stack it with your Nature bonus. Without more, a Poisoner’s Kit is a tough sell for a proficiency investment vs. a skill with broader application.

Crafting. For crafting purposes, the DMG points us to the crafting rules