In flutter, is there an option to draw a vertical line between components as in the image.
Not as far as I know. However, it is quite simple to create one — if you look at the source for Flutter's Divider you'll see that it is simply a SizedBox with a single (bottom) border. You could do the same but with dimensions switched.
Update (Oct 4, 2018): a VerticalDivider implementation has been merged in by the Flutter team. Check out the docs but it's very simple to use — simply put it between two other items in a row.