The speaker of "The Flea" is like, "Let's act like a married couple would act," and he's not talking about splitting the chores and fighting over the remote, either. He means he wants to do what a married couple would do – with the blessing of church, family, and state – in the bedroom. Ah, the "blessing" part is the rub, because without marriage, their act would be considered sinful in the seventeenth century. But from the perspective of a woman in Donne's time, marriage gave her security and at least some power in the relationship. Otherwise, the man could just take what he wants and hit the road. But our speaker would never do a thing like that, would he...?
The speaker does not actually hope to convince the woman that they are already married. Rather, he wants her to begin to imagine a hypothetical future in which they are linked together.
In the poem, marriage is more important as a religious and social ceremony than as the culmination of a romantic bond.