Archchronicler, catchphrase, eschscholtzia, latchstring, lengthsman, and postphthisic each have six consonants in a row. Borschts has six consonants in a row in just one syllable. Words with five consecutive consonants include angstrom, angsts, birthplace, dumbstruck, eighths, heartthrob, lengths, postscript, strengths, thumbscrew, twelfths, warmths, and witchcraft.

The longest word without a vowel is Twyndyllyngs which, although being Welsh and meaning 'twin', is in the OED.

Cheers

DeG