AFAIK, there are no rules for that. We can extrapolate the rules given for harvesting from other creatures, though.
Some poisons from the DMG can be harvested
For example, the Serpent Venom (DMG p. 258)
This poison must be harvested from a dead or incapacitated giant poisonous snake.
Most of these poisons don't state "from a willing..." because they are harvested from creatures that aren't likely to be willing, IMHO. I don't see how adding "willing" to the text would break anything.
In this case, the damage done by the poison (3d6) is equal to the damage done by the poison from snake's attack, so keeping the 2d6 is consistent.
Rules for harvesting
A character can instead attempt to harvest poison from a poisonous creature, such as a snake, wyvern, or carrion crawler. The creature must be incapacitated or dead, and the harvesting requires 1d6 minutes followed by a DC 20 Intelligence (Nature) check. (Proficiency with the poisoner's kit applies to this check if the character doesn't have proficiency in Nature.)
I would say that, for self-extraction, the creature knows enough about himself to be proficient with knowledge about himself, so you always add the proficiency bonus. The DC might also be lower, but that's your call.
Note on duration
Per DMG Errata, Injury Poisons (which usually are the harvested ones) say
Injury. Injury poison can be applied to weapons, ammunition,
trap components, and other objects that deal piercing or
slashing damage and remains potent until delivered through a
wound or washed off.
So while it's a fun idea, note that it is a one use only (per application). You can, obviously, restate that - but the reason this errata was added was because otherwise poison is broken. See Poison Bug (2014, pre-errata). In particular, Extra Attacks become insane.