Like most incarnations of the El family, Supergirl is able to hover and fly.
We know that Superman doesn't always need to be able to breathe in space, and there has been discussion about how Superman flies, but the 2015 Supergirl TV show appears to have different rules.
From Better Angels (S01E20):
You wouldn't be able to generate thrust, you wouldn't be able to breathe, you wouldn't be able to get back.
While one might argue
that this was just Alex conjecturing and trying to convince her to not go, Supergirl was briefly stranded once she left Earth's atmosphere.
Has there been any explanation as to how Kryptonians hover or fly in this newest version?