Firstly, of course, the object of ‘quench’ must be a thirst or desire of some kind—not the person who is thirsty or desirous. But I take it you know that, and that is why you say you’ve joked with your friends.
‘Quench’ is not a real equivalent for ‘feed’. The latter simply means to give someone food (whether it fills them up or not), while the former means to extinguish a thirst. In other words, ‘quench’ is the liquid counterpart to ‘sate’
I don’t know of a word that specifically corresponds to ‘feed’, but for liquid items; I would guess there isn’t one. But since you can say of babies that they feed on breast milk, and breast milk is liquid, I guess you might at a stretch be able to expand ‘feed’ to include liquids, too. I wouldn’t count on others to understand it out of context, though.
On a more historical note, ‘feed’ is in origin simply an i-umlaut causative¹ of ‘food’. If we apply this same strategy to ‘drink’, we arrive at a verb that does exist, but has developed a slightly different meaning over the centuries: drench.
So if you are just looking to joke with your mates, you might say, “I am hungry—feed me! I am thirsty—drench me!”
¹ In the older stages of the Germanic languages, i-umlaut, from the Proto-Germanic suffix -j(a), in its turn from the Proto-Indo-European causative suffix -ei̯e/o-, is the most common way of denoting causative verbs meaning ‘make someone do X’.