(At least as far as the current timelines go, since both shows have spent quite a bit of time in the past.)
Which would mean that Gotham’s relatively timeless setting takes place before much of what has happened on Arrow and The Flash.
Because it’s still the carrot dangling in front of the horse as far as what could be within the world of comic book TV connections.
Neither Arrow nor Gotham (or any of the other shows) have had any characters using Batman’s name willy nilly — Gotham is obviously building up its billionaire vigilante to eventually become the Dark Knight — but there have been quite a few instances where characters have referred to Gotham’s caped crusader with more generic references.