In this excellent story there are actually very few round characters. Remember that a flat character can be compared to a paper doll - they are two dimensional, with only one or two key personality traits. A round character has the three-dimensional qualities of real-life people, with many traits and complexities.
Given this distinction, let us consider how the characters in "The Doll's House" measure up. It is clear that out of the Burnell children, it is only Kezia who is a round character. The others are only interested in flaunting the Doll's House to gain standing amongst their friends and in mocking the Kelvey sisters. It is Kezia who shows she is a more rounded character, and the author gives us lots of information about how she is struck by the lamp:
But the lamp was perfect. It seemed to smile at Kezia, to say, "I live here." The lamp was real.
Kezia's focus on the lamp and her thinking about it show that Mansfield is presenting her as a round character.
When we consider the Kelvey sisters, at first they are presented as flat characters - easily distinguishable because of their way of walking and bearing themselves - Lil's silly smile and Else always hanging on to her sister. Yet, by the end of the story, we see that there is more especially to Else. Her comment about seeing the "little lamp" is highly significant, not least because the lamp is an important symbol in this story, but also because it shows that she is not the stupid, silent girl that everyone takes her for and she is able to think at a deeper level.