Longest English word without a vowel sound

All the words you mention have vowel sounds. I can think of no English word that doesn't have vowel sounds, except something like Mmm.

Debatable but there is a list on Wikipedia which seems to classify these based on dialect

Rhotic dialects, such as in Canada and the United States, have many words such as bird, learn, girl, church, worst, which some phoneticians analyze as having no vowels, only a syllabic consonant, [ɹ̩]. However, others analyze these words instead as having a rhotic vowel, [ɝ]. The difference may be partially one of dialect.

There are a few such words which are disyllabic, like cursor, curtain, and turtle: [ˈkɹ̩sɹ̩], [ˈkɹ̩tn̩] and [ˈtɹ̩tl̩] (or [ˈkɝːsɚ], [ˈkɝːtən], and [ˈtɝːtəl]), and even a few which are trisyllabic, such as purpler [ˈpɹ̩.pl̩.ɹ̩], hurdler [ˈhɹ̩.dl̩.ɹ̩], burglar [ˈbɹ̩.ɡl̩.ɹ̩], gurgler [ˈɡɹ̩.ɡl̩.ɹ̩], certainer [ˈsɹ̩.tn̩.ɹ̩], and Ur-turtle [ˈɹ̩.tɹ̩.tl̩]. The words wyrm and myrrh contain neither a vowel letter nor a vowel sound in these dialects: [ˈwɹ̩m], [ˈmɹ̩] (or [ˈwɝːm], [ˈmɝː]).

It is true that almost all English words have at least one vowel sound. The only exception (other than Hmmm, zzz, etc.) that I know is rng. A rng is an algebraic structure satisfying the same properties as a ring, without assuming the existence of a multiplicative identity. In short, a rng is like a ring without i (the identity element); which hopefully explains its vowelless spelling.