The director, James Gunn, has confirmed that the sequel takes place 2 months after the original movie....so 2014 which apparently dates it before Civil War (but see below).
However, we don't know the dates of the other MCU movies.
Kevin Feige to Comicbook.com
Yeah, knowing that outside of the Guardians franchise, we don't necessarily always date the movies. You don't always know, we don't say, '2012, 2013...' We do in the Guardians because you do the math and 1988, and it's 26 years later. But we never say, 'Oh, this takes place in 2018, this takes place in 2017.' But it was important for the story that James wanted to tell that they're still relatively fresh in their new group.