I believe Emily chose the fly for two main reasons. The first reason is a practical one. 'Fly' is a really easy one syllable word to rhyme with. Looking at how the word is used within the context of the language of the poem, 'fly' was a diction choice based on brevity of length and simplicity. Using some other sort of insect would have been tiresome and difficult; although she might could have used the word 'bee.' Bees also buzz.
Dickinson also probably chose the fly for its simple, common nature. Flys have the reputation for being slightly annoying creatures, always showing up when they are least wanted. Dickinson incorporates the fly to anchor her poem in a common occurrence that people could readily identify with.