What a fascinating question! I suppose we could argue that this excellent short story is a kind of literary descendant of Emily Dickinson's excellent poetry. What Dickinson's work does is present us with a singularly feminine view of the world. Her poems are told distinctly from a female point of view, and this is in contrast to the patriarchal view of the world which the majority of literature from this time presents us with. "The Yellow Wallpaper" picks this up, and develops it further, presenting us with an unreliable narrator who is female and struggles against the restrictions of being a woman in a patriarchal world in which everything is decided for he and which she has no power. From the very beginning of this excellent story, the narrator makes it clear that she is trapped in a number of different ways, but one way in which she is trapped is through her husband's insistence that she is not ill and that she must have rest and quiet. Her own thoughts and feelings are completely disregarded:
Personally, I disagree with their ideas.
Personally, I believe that congenial work, with excitement and change, would do me good.
But what is one to do?
If Dickinson records the realities of living in a patriarchal world from a female perspective, this story takes this one step further by showing overtly the ways in which a patriarchal world inhibits and impinges upon the freedom of the women that live in it. Therefore we can definitely argue that there is a relation between the work of Dickinson and this short story.