The spacing is set by a cam plate you can see under the sliding cover. If you aren't getting the counter correctly set to zero when you load, that will cause overlaps. The easiest way I know to fix overlaps, though, is to put a wrap or two of tape on the spool core before loading the cassette. You could also advance a couple more frames before resetting the counter.
Either way increases the core diameter, which will increase the amount of film advanced (Kiev is a turns-counting mechanism), and increase spacing throughout the roll. If you have spacing that increases through the roll, us thinner film (slit from 120 instead of 35mm, for instance); vice versa use thicker film to prevent late-roll overlaps (slit from 35mm). Film thickness interacts with initial core diameter, too -- the bigger your core, the more film builds up as you advance (because it'll advance further), so the less your spacing will shorten (or the more it'll increase),
And then there are Minolta cassettes in a Kiev; the larger core will result in wide spacing, possibly running out of film before the counter runs out.