Batman (Comics, TV, and Movies)

In the 1989 film version of Batman (directed by Tim Burton), there is a brief scene that takes place in a government's office (either the mayor's of the District Attorney's one). Behind the desk are a US national flag and another flag. The flag has the words "GOTHAM STATE" on it so what it represent is easy enough to guess and the general design is that of the US state of Indiana but in a simplified manner.

A similar flag is seen earlier on a podium during a speech by Harvey Dent which seem to be a variation: more stars and the word "GOTHAM" only. Considering how briefly it is seen and the fact is is folded, it's hard to tell if it is the same one but looking different due to the way it's scrunched up or if they needed an extra one and someone simply went out and bought an Indiana flag and sticky taped "GOTHAM" on to it.
Marc Pasquin, 20 November 2014

It's a very dark blue ~2:3 flag with a small seal image centered on it surrounded by a wide ring of 13 small golden yellow stars pointing outwards (the ring seems to be assymetrical as a whole, i.e., there is no one star at the noon position).

The seal disc shows a sailship with "1620" in white on the sea. This is surrounded by a blue ring fimbriated white, seal-style, reading something in yellow capitals; behind the disc two crossed swords pointing upwards and a coil of rope edging it; laurel wreath made of two branches tied below and over the bottom part of all this a large golden yellow scroll reading "Gotham" in black serifed capitals.
António Martins-Tuválkin, 22 June 2008