Is it permissible, from a Sharia perspective, to slaughter old chickens that are no longer profitable and feed them to dogs and birds of prey, or is it better to feed them to the poor and needy, knowing that charity should be from the best of one's wealth?

If there are poor and needy people who accept old chickens, then feeding it to them is better and brings a greater reward than feeding it to animals. The noble verse: "O you who have believed, spend from the good things which you have earned..." does not indicate the unlawfulness of giving charity from inferior things voluntarily, but rather indicates the desirability of giving charity from good things. The verse is interpreted as referring to the intention of giving away inferior things, not to giving it away incidentally without intention. Therefore, giving old chicken as charity is permissible and rewarded, Allah willing.