Whether Emily Dickinson was a feminist poet depends on the definition of feminism one uses. In one sense, "feminism" means to participate in organized activity advocating for women's rights and interests. In another sense, "feminism" means simply a belief in equal rights and opportunities for women. There is no indication that Emily Dickinson was a feminist in the first sense of the word. Since she lived most of her adult life in a semi-reclusive state, she did not become involved in public efforts for women's suffrage, for instance.
However, one could build a case that Dickinson was feminist in the second sense of the word. Dickinson's poetry deals with a wide variety of topics that affect women and men equally. Her poems about death, grief, nature, faith, and other philosophical topics reflect a woman of high intelligence who was the equal of any male poets writing in her day, or any other day. Interestingly, Dickinson was not beyond assuming a male persona in her poems, as evidenced by "A narrow Fellow in the Grass" (1096), but there are other poems in which the speaker is obviously feminine, such as "I'm wife - I've finished that -" (225). Because of her primary subject matter, her poetry could be considered feminist because it treats men and women equally in that all are equally affected by the issues she writes about.
As far as Dickinson's personal life, she never married but devoted her life to her writing career. Although she published only a few poems in her lifetime, she was an assiduous author, producing nearly two thousand poems. Upon her death, her family found 40 volumes of poems she had bound into fascicles by hand, so she was pursuing her writing career intentionally, even though no one understood at the time to what extent.
By looking at the subject matter of Dickinson's poetry and considering her personal life, one could make the case that Dickinson was a feminist writer who believed in the equality of the sexes.