I've commented it in the other post, but in my opinion, this looks more like an informal fallacy, not a logical one.. because the issue is that in between lines (specially in the context for which it's used) it seems to want to imply that having something to hide must be something rare or perhaps wrong.. as if it were not possible to want to hide things that are good for society to keep hidden.
This isn’t a formal, logical fallacy, but an informal one: https://en.wikipedia.org/wiki/Informal_fallacy
From a perspective free of presuppositions and biases, I don't think the argument on itself is wrong, because of course I wouldn't be worried about my privacy if I had no interest in keeping my private information hidden.... but the context in which the argument is used is the problem.. not the logic of it.
It's not incorrect to say: "nothing to hide" -> "No reason to be worried of showing it" ...what's incorrect is assuming that the "nothing to hide" antecedent is true for all law abiding citizens ...as if people didn't have an interest in keeping perfectly legal and legitimate things hidden. So it's not that the statement isn't logically sound, the fallacy is in the way that it's used, they are pretending that this means people shouldn't be worried, when in fact it means the opposite, since everyone does, in fact, have information that should remain hidden. For our own safety and the safety of our society!