The Gurevich paper you cite was translated as "Some Existence Conditions for K-Decompositions for Special Flows" in Trans. Moscow Math. Soc. 17 (1967), 99-128 (if you don't have access to a university library I can send a copy to you; you can find my university email address by searching my name). There is also the Totoki paper as mentioned in the comments. Totoki also has a book titled *Ergodic Theory*, which includes the argument in the paper without much change it seems. Ornstein and Smorodinsky's paper "Ergodic flows of positive entropy can be time changed to become $K$-flows" has an argument very similar to Totoki's argument.

Sinai's two papers "Dynamical systems with countable Lebesgue spectrum " I and II are the standard references for $K$-flows.

Katok has a related paper titled "Smooth Non-Bernoulli $K$-Automorphisms" where he interprets the $K$-property for skew products as a cohomological equation. (This paper uses smooth structures; instead of being purely ergodic theoretical.)

Finally, most ergodic theory books don't include flows at all; one book that does is Cornfeld, Fomin, Sinai's *Ergodic Theory* with a special emphasis on the connection between $K$-property and spectral properties (there is also a chapter on special flows; but the connection between $K$-property for special flows and the $K$-property for the base automorphism is not developed). Nadkarni's *Basic Ergodic Theory* also has a chapter on flows; but it does not have anything on the $K$-property.

1more comment