You have to be careful with the interpretation of energy when you don't know what sort of gravitational potential well might be involved. For example, you might find some amount $m c^2$ of rest-energy of matter when calculated in an inertial frame near but outside the horizon of a black hole, but in order to use this energy at some other location, you would first have to pull the matter up against gravity, expending energy $E$ in order to do so. After spending that $E$ you acquire just $m c^2$ at your location, so overall you have gained $(m c^2-E)$ and this will be small compared to $m c^2$ if the matter started out near a horizon. This is the sense in which gravitational binding energy is negative. When applied to the whole universe, this consideration makes a calculation of the type you are proposing questionable, because it is hard to say what physical meaning it has.
A better analogy is, perhaps, with the concept of escape velocity. A flat universe is one where the motion of matter everywhere is just enough to keep escaping from its own mutual gravity.
Finally, the topology of a mathematical space is not in one-to-one correspondence with the curvature, and in particular, if a space is flat it does not necessarily follow that it is infinite. There are a number of different topologies that are mathematically possible for a flat space, and some of them are bounded (i.e. not infinite). So this may apply to the physical universe too. We don't know.