This study investigates the influence of cone rotation on boundary-layer instabilities in supersonic and hypersonic flows using linear stability theory. In a rotating reference frame, the linearized disturbance equations include terms representing Coriolis and centrifugal forces, whose effects on primary instabilities—such as the first and second modes, crossflow, and centrifugal instabilities—are only partially understood, particularly for compressible flows. The results reveal that rotation destabilizes all instability modes, with the centrifugal instability becoming dominant at higher rotation rates. While centrifugal and metric terms, the latter accounting for surface curvature and conical divergence, exhibit stabilizing effects, Coriolis forces act as a destabilizing mechanism.