  We study flows on C*-algebras with the Rokhlin property. We show that every
Kirchberg algebra carries a unique Rokhlin flow up to cocycle conjugacy, which
confirms a long-standing conjecture of Kishimoto. We moreover present a
classification theory for Rokhlin flows on C*-algebras satisfying certain
technical properties, which hold for many C*-algebras covered by the Elliott
program. As a consequence, we obtain the following further classification
theorems for Rokhlin flows. Firstly, we extend the statement of Kishimoto's
conjecture to the non-simple case: Up to cocycle conjugacy, a Rokhlin flow on a
separable, nuclear, strongly purely infinite C*-algebra is uniquely determined
by its induced action on the prime ideal space. Secondly, we give a complete
classification of Rokhlin flows on simple classifiable $KK$-contractible
C*-algebras: Two Rokhlin flows on such a C*-algebra are cocycle conjugate if
and only if their induced actions on the cone of lower-semicontinuous traces
are affinely conjugate.
