Of course we have not to think to much about most time travel stories, otherwise we will find inconsistencies and logical breaches all over the place. But what beside other things comes to my mind when watching legend of tomorrow is the following:
Rip Hunter takes the main characters out of their timeline in 2016. In the future they meet friends (like Arrow) but they never meet themselve. In the future it seems that they disappear in 2016. But they seem not to be concerned about that could mean they never made it back to 2016. So if they succeed in their mission and return safely to 2016, this would change the futures they visited, because now they didn't disappear in 2016 and never came back. This kind of logic seems to imply, that things you do later that change the past (like returning to 2016) have not happened yet and the timeline does not respect it. Therefore the future where they met Arrow and where they all have disappeared in 2016. But if we look now at the case of Chronos, this logic does not hold true. Chronos pursuits them from the beginning, in spite of being "created" by them much later. So in this case, some change of the timeline they will do later, already has happened and affects them.
So how exactly do changes of the timeline work in the show?