Can a MITM attack be applied to this construction?
Let $K^1,K^2$ be the key-streams generated by $k_1,k_2$.

Now define $E^1_{k_1}(m):=m\oplus K^1$ and $E^2_{k_2}(m):=m\oplus K^2$.

Note that $E^1_{k_1}(E^2_{k_2}(m))=m\oplus K^1\oplus K^2$.

You now have a straight double encryption and can apply the standard meet-in-the-middle attack now.



The implementation would use a known-plaintext pair $(m,c)$. You would now tabulate all $E^1_{k_1'}(m)=m\oplus K^{1'}$ and then try all $D^2_{k_2'}(c)=c\oplus K^{2'}$ and look for matches between $E^1_{k_1'}(m)$ and $D^2_{k_2'}(c)$.