A k-slug is essentially a high-velocity bullet. The conventional wisdom on k-slugs is that they don't work in space because your target moves literal kilometers just in the time it takes your bullet to move down the barrel. This is a bit of an exaggeration. If you're rendezvousing with the enemy anyway, the relative velocity is low--probably less than several hundreds of m/s. An ordinary bullet moves a bit faster than this, and a k-slug probably 3-10x as fast again. However, the problem is real.
The solution is to lead your target. As above, an opponent can't really dodge effectively. But, the inaccuracy of projectile weapons means you're pelting an entire volume with k-slugs anyway, so a bit of jitter from enemy maneuvering is essentially meaningless.
Note: CoaDE models k-slugs with railguns and coilguns, which I think are probably optimistic/unrealistic (some versions fire >100 / sec, including cooldown). They also make an argument for tracer rounds on every shot, since stealth is meaningless in space. I disagree; tracer pyros are extra mass you need to accelerate, and ballistics computers have essentially no use for visual confirmation of a hit.
K-slugs are effective at any range, though obviously accuracy decreases as range increases. It's mainly a question of how much mass, in the form of k-slugs, you can afford to have miss.
Example: a base in a hollowed-out asteroid will be willing to fire k-slugs at any distance. This opens the door to interplanetary-scale bombardment.