Some stories tell well from beginning to end, all in a neat little line...and some don't.
When can a story be improved by using a different order in the telling?
Off the top of my head, I'd say flashbacks are great when something doesn't make sense out of the context of what is happening now in the story, or when something that happened long ago (before the story's timeline begins) is important to the story.
Also, in a project I'm working on, the story begins at a point where it is very hard to introduce the characters well, so I started at a point after that, then transitioned to a flashback on how they got to that point. It seems to be working out well.