Let $E$ be a semantically secure cipher.
Let $E'(k,m) = E(k,E(k,m))$.
How would one prove that $E'$ is not necessarily secure even if $E$ is?
It doesn't make sense to me. If you consider the advantage of an attacker $\mathcal{A}$ over a semantically secure cipher $E$, you have $SSadv[\mathcal{A},E] = \epsilon$, where $\epsilon$ is negligible.
If you call for $E(k,E(k,m))$, you should have $E(k,E(k,m)) = E(k,c)$, where $c$ is $\epsilon$-distant of being random, so you give an advantage of $\epsilon$ to the attacker.
When you compute $E(k,c)$, analogously you give another advantage of $\epsilon$ to the attacker, so you give an overall advantage of $(\epsilon + \epsilon)$, and such a sum would be negligible as well.