I haven't watched it yet, but looked at some descriptions online (including the Arrowverse Wikia) - evidently, they've made some changes (Astra's race changed from African American to Caucasian, Chas's country of origin). So evidently it is not in Arrowverse continuity.
As I said, it's not entirely clear which version of Constantine is the one in the Arrowverse. There are subtle hints that it's the live-action series, but the onscreen evidence is inconclusive, since neither Arrow nor Legends of Tomorrow has clearly referenced anything that's unique to either series -- just the general John Constantine backstory that both versions share.