Breaking zero knowledge protocol for graph hamiltonicity
The protocol for Hamiltonicity is by Blum and not FLS (FLS indeed use it). The protocol as you presented it is zero-knowledge for a malicious verifier as well. However, it is not known to be zero-knowledge when run in parallel (in order to get negligible soundness error). On the flip side, we also do not know how a dishonest verifier can do anything. 

What do we know about the parallel repetition of Hamiltonicity? 

First, we know that it is not black-box zero knowledge; see On the Composition of Zero-Knowledge Proof Systems.

Second, it is possible to prove that $log^2 n$ repetitions of the proof is actually zero knowledge in the unlikely case (not believed to be true) that Circuit-SAT on $n$ variables can be solved in time $2^{\sqrt{n}}$. This demonstrates that it would be very hard to prove that this protocol is not zero knowledge, without proving strong lower bounds on CSAT (note one could theoretically prove this under such an assumption, but no one knows how to do this). This proof can be found in Section 8 of Lower Bounds for Non-Black-Box Zero-Knowledge.

Third, we can prove that parallel Hamiltonicity is witness indistinguishable.

Finally, it is clearly honest-verifier zero knowledge.