Gotham sits in a stylised universe that is timeframe agnostic. Cars are 70s looking yet they have mobiles from the 2000s. There's a deliberate lack of any use of computers or mentioning of any dates, but the computers that do exist (Bruce's house) are clearly bang up to date style machines.
Arkham uses therapies that would have been considered outdated in the 60s, yet has technology that is more advanced than we have today.
Gotham sits in its own world where it's not meant to exist in any single recognisable point in time.
See I thought the Suicide Squad in the films was from the same universe as of that in Arrow, just that they were using A-list actors for the film rather than those from the TV show.
Looks like I was wrong
This is what started to throw me. They are in Arrow but that isn't who is in the film. The Flash in Justice League isn't the one in the TV show, yet both will be on at the same time. Deadshot is still floating around the Arrow/Flash universe isn't he?
Marvel have some conflicts which are quite well handled (the removal of 'mutant' as a term from the MCU and 'the twins' never being called Quicksilver or The Scarlet Witch so it avoids the casual viewer (my GF) getting confused). DC just seem to be handing out franchises all over the place, pushing out as much as possible across as many platforms as possible and its confusing (me anyway) more than helpful.
And then there's Deadpool who just 4th walls his way through all of it, mocking the other version of himself and the Green Lantern, the licensing and generally being awesome lol.