It is exactly the content of a paper of Minami At least for compact Lie groups)

https://projecteuclid.org/journals/osaka-journal-of-mathematics/volume-6/issue-1/A-K%C3%BCnneth-formula-for-equivariant-K-theory/ojm/1200692333.full

Following ideas of Atiyah's proof of the Kunneth theorem for K-theory (non-equivariant) he obtain exactly the result you want.

As a final comment note that if $G$ acts on spaces $X$ and $Y$ it is too much hard to obtain $K_G(X\times Y)$ in terms of $K_G(X)$ and $K_G(Y)$

It is exactly the content of a paper of Minami (At least for compact Lie groups)

A Künneth formula for equivariant $K$-theory. Haruo Minami. Osaka J. Math. 6(1): 143-146 (1969).

Following ideas of Atiyah's proof of the Kunneth theorem for K-theory (non-equivariant) he obtain exactly the result you want.

As a final comment note that if $G$ acts on spaces $X$ and $Y$ it is too much hard to obtain $K_G(X\times Y)$ in terms of $K_G(X)$ and $K_G(Y)$