There are no common English words with 6 consonants and no vowels. However, the compound words archchronicler, catchphrase, and latchstring all have 6 consonants in a row.
bath back bass bark ball bask bash balm barn bank cart can't calm cast call cash dash dart dank dark darn (to sew) dawn farm fact fall fast fawn gash gall hall malt hard harp harm hash jazz jack lark...