How do figures of speech contribute to the poem's overall intentions?
The first problem is that we have no actual access to the poet's intentions. Dickinson did not leave any written explanation of what she intended in writing the poem, and a poem itself, while capable of expressing the intentions of a human author, is not itself a living being capable of having intentions. Thus we can only describe accurately the effects a poem might have upon the reader; any claims about the poet's intentions are purely speculative.
The personification of Death has been a feature of art and literature for several thousand years. While death is universal, in the sense that all living beings eventually die, it is also mysterious, as death is not comprehensible; death by definition is cessation of the functions of the brain necessary for comprehension. Thus a poem can only address death by metaphor.
Dickinson's use of the device of personification in some ways domesticates death by portraying it as the driver of a carriage that takes the narrator on the journey from ordinary to eternal life. Rather than trivializing Death by giving a detailed description, she uses the term "kindly" to suggest that Death should not be feared.
The idiosyncratic use of dashes makes the reader pause frequently in reading. It suggests a struggle on the part of the poet to articulate a sense of something beyond mortal knowledge. It also makes the reading experience odd and alien to normal reading.
The alliterative pairings yoke together concepts and add to the musicality of the poem.