The list of clean animals that Israelites could eat can be found in Leviticus 11 and Deuteronomy 14.
In those lists, God specifically talks about which birds are not to be eaten.
"You may eat any clean bird. But these are the ones which you shall not eat: the eagle and the vulture and the buzzard, and the red kite, the falcon, and the kite in their kinds, and every raven in its kind, and the ostrich, the owl, the sea gull, and the hawk in their kinds, the little owl, the great owl, the white owl, the pelican, the carrion vulture, the cormorant, the stork, and the heron in their kinds, and the hoopoe and the bat. And all the teeming life with wings are unclean to you; they shall not be eaten." (Deuteronomy 14:11-19)
So chickens are not included in the banned birds list. While chickens do eat worms and various insects, they do not actively feed on dead animals nor do they hunt for other birds or mice. The unclean birds listed either eat dead animals (e.g. vultures) or they are hunters or predators (e.g. eagles).
However, God did not explicitly state the criteria for clean birds. God only said what birds may NOT be eaten. So any generalizations are only guesses on why certain birds are allowed or disallowed.
In both lists of clean foods, God does not say why certain animals are clean or unclean. Although we can make guesses that unclean animals are less healthy to eat, we need to remember to let God be God. He may not explain all His commandments as to why He made them. We just need to respect that and obey Him.
Sometimes He tests us on whether we would obey Him even if we don't know why.
Christians are not required to keep strict laws on food like the Israelites did. However Christians are told to avoid blood, things sacrificed to idols, and animals that are strangled (Acts 15:28-29).