  By extending the standard holographic principle to a cosmological framework
and combining the non-flat condition with the Kaniadakis entropy, we construct
the non-flat Kaniadakis holographic dark energy model. The model employs
Kaniadakis parameter $K$ and a parameter $c$. Derivation of the differential
equation for KHDE density parameter to describe the evolutionary behavior of
the universe is obtained. Such a differential equation could explain both the
open as well as closed universe models. The classification based on matter and
dark energy (DE) dominated regimes show that the KHDE scenario may be used to
specify the Universe's thermal history and that a quintom regime can be
encountered. For open and closed both the cases, we find the expressions for
the deceleration parameter and the equation of state (EoS) parameter. Also, by
varying the associated parameters, classical stability of the method is
established. On considering the curvature to be positive, the universe favors
the quintom behavior for substantially smaller values as opposed to the flat
condition, when only quintessence is attained for such $K$ values.
Additionally, we see a similar behavior while considering the curvature to be
negative for such $K$ values. Therefore, adding a little bit of spatial
geometry that isn't flat to the KHDE enhances the phenomenology while
maintaining $K$ values at lower levels. To validate the model parameters, the
most recent $30\;H(z)$ dataset measurements, in the redshift range $0.07 \leq z
\leq 1.965$ are utilized. In addition, the distance modulus measurement from
the current Union 2.1 data set of type Ia supernovae are employed.
