The short answer: It is its own canon, just as nearly every Batman that came before it.
The long answer: Batman is one of the most prolific DC characters to date, and has had numerous different interpretations. You can read more about them here. Unless otherwise stated, these each fall into their own separate canon, including:
Batman Comic Books
The DC Comics/Detective Comics canon for Batman spreads about as far and wide as comic book history itself, has had numerous spin-offs, and has changed multiple times.
Batman TV Series
The original Adam West TV show, which spawned its own movie.
Tim Burton Batman Movies & Sequels+
Includes the original Tim Burton's "Batman", "Batman Returns", "Batman Forever", and the now-infamous "Batman & Robin".
Chris Nolan's Batman Movies
Includes the new series of Batman movies, including "Batman Begins", "Batman: The Dark Knight", and "Batman: The Dark Knight Rises", as well as a direct-to-video animated feature "Batman: Gotham Knight".
The DC Animated Universe
Consists of numerous DC Cartoons, notably from Batman's standpoint "Batman: TAS", "The New Batman Adventures", "Batman Beyond", "Justice League", "Justice League Unlimited", and a number of cameos in other animated series.
Arkham Series Video Games
Most video games are one-shots that are derived from other works and don't connect to any other series, but the Arkham series of video games is notable for having its own continuity, including "Arkham Asylum", "Arkham City", "Arkham Origin" and "Arkham Knight".
The live-action show "Gotham" falls outside of all of these canons. Though what all of these canons share in common is that they are based off of the previous works. As pointed out by Richard, it is the artist's discretion which source to follow when writing new material for a separate canon. So it is well within the liberties of the show to introduce new characters.
+As pointed out in the comments, Tim Burton had nothing to do with Batman & Robin specifically.