Can you cancel out an EMP with another EMP? Say you had two explosively pumped flux compression generators facing one another. Once detonated, will the EMPs created by the devices cancel each other out or amplify each other?
 A: One EMP cannot cancel out or add to another unless at a point where the distance to the two sources is the same, or unless there is prior knowledge of when and where the first EMP occurs.
The reason is that the electromagnetic pulse travels with the speed of light.  The second EMP source would need to detect the first EMP, analyze it, and then emit a second EMP tailored to cancel the first EMP.  But by that time the first EMP would have passed beyond the second EMP source, and there would be no way for the second EMP to catch up with the first EMP in order to cancel it.
However, a set of EMPs could be emitted simultaneously from, say, a hemispherical shell, so that they simultaneously converged at the center -- and their intensities would add there. To use interference (addition of vector amplitudes) would be difficult, but not impossible.
A: If the EMP generators act as point sources (even as directed point sources) of radiation, they can destructively interfere only at isolated points. In other words, any finite volume will have a nonzero amount of power radiated into/through it. 
This is because points of destructive interference from two approximate point sources are exactly the points where two circles centered on each source would intersect. The intersection of two non-concentric circles is always a set of a few isolated points. And you can't just choose any two circles, either - the circles have to have radii compatible with the signal from one being exactly out of phase with the other, which leaves only a discrete set of pairs of circles as possibilities. So in the end, you have a discrete set of a bunch of isolated points.
A: Yes the EMPs would interact with each other just like waves do. The type of interference would depend on the phase difference between the EMPs. If they are in the same phase, their amplitude would double. If they are at a phase difference of ${\pi}$ they will cancel each other out (similar to how active noise cancellation works).
