tl;dr: No, Gotham is separate, as isare iZombie, but the and Lucifer. The rest of the DC shows are all effectively in the same universe (or multiverse, to be precise). Also, note that none of these shows are considered part of any movie universe (e.g. none of them are part of the DCEU)
In the 2014-2015 and 2015--2016 TV seasons, there's a ton of DC shows on the air:
- Arrow
- The Flash
- Constantine
- Gotham
- iZombie
- Supergirl
- Legends of Tomorrow
- Lucifer
The only explicitly shared universe in that group is the "Arrowverse" which includes the three shows aired on CW and produced by Greg Berlanti, Andrew Kreisberg and Marc Guggenheim: Arrow, The Flash, and Legends of Tomorrow.
At Comic Con 2014 it was stated that there's no shared universe among the others, as of yet:
While we know that Arrow and The Flash will crossover a lot, it was deemed a little difficult to cross over the non-CW shows, since Gotham's time period is a little uncertain. Gotham executive producer Bruno Heller said, "Never say never" but pointed out "If those two [Gotham and Constantine] worlds coincided, then it would work. But I'm not really sure of the chronology. Maybe Constantine is only five when Gotham takes place."
So far, iZombie, Lucifer and Gotham have remained separate, and their setting and tone are diverse enough that they'll probably remain that way. However, after Constantine was cancelled by NBC, Berlanti's team got Matt Ryan to reprise his lead role on S4E05 of Arrow, meaning that Constantine retroactively joined the Arrowverse. In addition, in S01E18 of Supergirl (also produced by Berlanti's company), Grant Gustin appeared as Barry Allen, also bringing Supergirl into the Arrowverse continuity.
