Adding on: The recipe was changed when the need for specifically raven feathers for a Hilde quest was added in 3.2x. Before that it was cheaper to buy the potions from Daiyu (50 coins) than the ingredients to make your own from Makith (60 coins for two spider eggs, +10 more if you needed blue lilies as well). Now it's just 30 coins for one spider egg plus the feathers.You need to sneak up on Ravens from behind. Come in from the front or sides & they fly away. Catch one from behind and you're good.
Dunno if Tinkerer even thought about whether chicken feathers could be used for the potion. I suspect not...Agility potions are about improving your reflexes and chickens aren't exactly nimble.