Do frogs eat baby flies

No, all amphibians feed only on live prey (well, in the wild that is, though there are techniques to trick an amphibian into thinking an animal is alive).

Actually, all amphibians do not feed only on live prey. There are some species of toads which eat dead animals, and even leftover dog food or cat food. This is a common problem in the northern half of Australia, where introduced cane toads are rampant, and pose a danger to pets.