Kendra Saunders committed suicide and then her body was possessed by the soul of the Golden Age Hawkgirl, right?
That's what Wikipedia says, but apparently CW Superhero Series to Be Named Later is just making her the latest reincarnation of Hawkgirl.
Well, the thing is there was some mystery about Kendra in the JSA ongoing. Or at least the whole "possessed by Shiera Hall after committing suicide" bit was revealed later, so if they're going with the same basic character arc for her this Kendra might be saving that for a reveal.
On the other hand the whole "growing wings out her back" and "ancient warrior persona manifesting" is completely new, so... never mind.
Reincarnation of ancient warriors is part of the Hawkman mythology.