How does a Vow of Silence relate to Nietzsche?

I have to give credit to this article, which phrases it better than I could.

Dwayne is Olive’s angsty teenage brother, shown early on reading Nietzsche’s Thus Spoke Zarathustra and wearing a shirt that reads “Jesus Was Wrong.” He even has a wall-sized painting of Nietzsche hanging on his bedroom wall. Dwayne takes a vow of silence inspired by the great philosopher, using Nietzsche’s radical energy and idea of the Übermensch to channel his disdain toward others. As an angry teenager, Dwayne understands nihilism as a reason to hate the world and everyone in it.

In short: Dwayne hates the world (in classic teenager fashion), and expresses that by partially refusing to engage the world, essentially giving it the silent treatment.

However...

But at this stage Dwayne misunderstands Nietzsche, whose nihilism was not a rejection of life but an affirmation of an authentic life unbound by false values.

In short, Nietzsche's actual conclusion is closer to the ending of the movie, where the family all have decided to let go of their expectation and instead live life as it comes.

Coincidentally, Nietzsche spoke out against keeping silent, a point that very much highlights how Dwayne's silence is not in line with Nietzsche's thinking:

• "Silence is worse; all truths that are kept silent become poisonous."
• "For both parties in a controversy, the most disagreeable way of retaliating is to be vexed and silent; for the aggressor usually regards the silence as a sign of contempt"

To be fair, Dwayne does actually feel contempt for the world (in classic teenager fashion), but he seems to have cherrypicked Nietzsche's words by choosing his vow of silence.

The only bows of silence I know of are by religious communities and not athiest ones.

Moreover, there is nothing in This Spake Zarathrustha about vows of silence. If anything it's' s book of prolix lyricism adapted from a Persian model like, say, Hafiz, whom Goethe is known to have admired; more, Nietzsche is known to have admired Goethe as an example of an artistic ubermensch; but it's unlikely that Goethe would have have returned the compliment given his warning about hubris in his Faust and which Nietzsche ignored and also because of the wrong-headed liberties that Nietzsche took with the notion of truth: Zarathrustha is known not to have spoken like that and also he's known to have founded Zoroastrianism on truth as a supreme value.

Given Nietzsche is something of a fad amongst artistes it's not surprising that a young angsty teenager - perhaps an alter ego of the writer himself - is seen to be getting off on him. Though, to my mind, given the secular turn in the West starting in the Renaissance it hardly seems a rebellious attitude ...

Most likely the director is probably trying to draw a parallel between atheism and religion by suggesting that an athiest can have a vow of silence. That is, by suggesting just as religion is taken seriously, so should atheism.

Nietzchean Zarathustra is a prophet who speak against moral duality (or not against but show that there is more than just two of those): Good-Altruism versus Bad-Egoism.
But about what Dwayne would talk if everything he would like to say have already be told (in a form of Nietzsche books)? There is nothing more he could say that haven't been said and it's kind of nihilistic view that it's not a problem of arguments (in this case what could be said to convince anyone) but self-fear and the unwillingness to abandon dualistic view of morality.

In other word: When you will loose the shackles come to me and we will talk.