It's not going to be so easy, if you want anything better than a very crude estimate. The + and - charges indicated on illustrations of molecules depict a relative absence or gathering of electron probability clouds in the region, respectively failing to balance with the positive nuclear charge or overwhelming it. You'd have to know the wavefunctions of the electrons, their molecular orbitals, and compute integrals over those all pairs of volume elements in the clouds for both regions.
As a practical approximation, there might some sense in using some average central point, a sort of center of mass, for each charged region of each molecule, and apply Coulomb's law. But this isn't likely to be accurate. It could be if the charged regions were spherical, then just as with gravity the integrals work out to be the same as the simple Coulomb's law. Unfortunately molecules aren't shaped like that.
If you are wanting to know the force between two molecules, or parts of a molecule, you should know that the charged regions will change shape - as the molecules move closer, the electrons, and whole atoms, "feel" the presence of other charges and are tugged. The molecules will electrically polarize each other.
So, instead of using Coulomb to estimate the force, it's better to calculate the electrostatic potential energy as a function of position, accounting for the way the molecules will distort each other at any given distance.
Of course, even better is to do a full-blown quantum mechanical calculation including spins and fully anti-symmetric wavefunctions and all that, but for DNA or even just a single base pair, that's a lot of number crunching.
