What seems to be the speaker's purpose in "The Flea"?
The speaker in this poem is trying to seduce a young woman to have sex with him, and he is using the flea to bolster his argument. While this may seem like a rather unconventional choice for a love poem, Donne makes it work. The clever metaphor and argument make this a great example of a metaphysical poem.
The speaker opens his argument by commenting that a flea has just bitten the speaker and then the woman, so "in this flea our two bloods mingled be." He goes on to explain that to his way of thinking, this is not "a sin, nor shame, nor loss of maidenhead." Therefore, since that is true, it would be OK to have sex because their blood is already mingled in the flea (they are one there) so they might as well be one in other ways. Elizabethans believed that there was blood exchanged in intercourse which furthers the logic of this sentiment.
The woman has put her hand up to swat and kill the flea, and he tries to stop her (and further bolster his previous argument) by suggesting and killing the flea would be like killing a part of both of them because they (their blood) is contained in the flea.
Even once she kills the flea, the speaker is not deterred. Now he says points out that since killing the flea didn't have any negative affect on either of them, either will her having sex with him. She had "false fears" that the flea their mixed blood in the flea meant a loss of honor, but now it seems that she won't lose anything by being with him.