You are absolutely correct. KH instability requires the following conditions: two uniform flow of different velocity and density that are incompressible and inviscid. The instability sets in when the following instability condition is met.
(U1-U2)^2 > g(rho1^2 - rho^2)/(alpha * rho1 * rho2)
alpha = 2*pi / lambda,
lambda is the wavelength of the disturbance,
subscript 1 and 2 refer to fluids 1 and 2.
This instability manifests as roll-up vortices examples of which include the famous Jupiter's Red Spot and cloud formation.
I hope this helps.
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