No, she didn't - Emily Dickinson saw fewer than twenty of her 1,775 poems published during her lifetime: when she died in 1886, her obscurity as a poet was nearly total. While many of her literary peers ( Emerson, Whitman) achieved notoriety, “the woman in white” remained virtually unknown—by choice. The startling originality of her poems doomed her work to obscurity in her own lifetime.
Her family did NOT burn any of her poems - her sister, Lavinia, did burn many of her letters, after Emily's death, at Emily's request.
Dear Ink Hollow - there seems to be some dispute as to how many of her poems were published:
"Dickinson's poetry presents the editor with a unique set of problems. Only eight of her poems were published during her lifetime (all anonymously and probably without her knowledge.) the rest being circulated in manuscript form among her friends and family"
"By her death (1886), only ten of Dickinson's poems (see: Franklin Edition of the Poems, 1998, App. 1) had been published. Seven of those ten were published in the Springfield Republican."
"During her lifetime, she published only about 10 of her nearly 2,000 poems, in newspapers, Civil War journals, and a poetry anthology."
"None of her poems were published during her lifetime . . "
So, I guess we can "pick a number between none and ten."