When does a fly look like its parent?

It is as an adult that a fly looks like its parents.

Specifically, flies go through a life cycle of complete metamorphosis. The metamorphosis is complete because it involves four stages (egg, larvae, pupa, adult). The fly looks different in each stage, as opposed to an insect which undergoes incomplete metamorphosis (three stages of egg, nymph, adult, in which the nymph is a miniature version of the adult).