To find the kashrus status of an organism, we first need to correctly classify it as plant, animal, of, or fish, as each group has its own distinct requirements. E.g., animals need to chew cud and have cloven hooves, while fish need (fins and) scales.
What is the halachic definition of a of (עוֹף)?
Note that many translations have both a bat and an ostrich listed as "birds". As an example, Rabbi Aryeh Kaplan in Living Torah and the English translator in Rav Hirsch (his grandson Isaac Levy) use Bas Haya'ana as ostrich and ataleif as bat. These translations state that both an ostrich and a bat are halachically considered "of". Thus it appears that a bird is a "winged animal" whether or not it flies. A penguin would seem to be similar to an Ostrich in that it is a flightless winged animal.
Actually, if one wants to analyze a flipper and a wing, one could say that a fish "flies" through the water or a bird "swims" through the air. In both cases, they are propelled through the external medium by something very similar.
