The question could be interpreted as being about "vowel letters". "Twyndyllyngs" is a candidate: said to come from Welsh. If we take "vowels" to be the letters [ieaou], then Norwegian råbygg has no vowels. The defect in the reasoning there is that in Norwegian, y, å, ø, æ are also "vowel letters", so you have to assume some definition of "vowel letter" for each language. Then in Arabic you write sentences without vowels: رأيت الكلب , although there are some diacritics that allow you to mark vowels, which are used in the Qur'an and in language-teaching materials. In Tigrinya, a word like ባልዶንጓ "beans" has no vowel letters – because every letter is a combination of a consonant and a vowel. And then there is the fact that Chinese writing (characters, as opposed to pinyin romanization) doesn't have letters at all. So the question might need to be limited to alphabetic systems (excluding Arabic, Tigrinya, Chinese), and then we'd need to define the vowel letters individually for each language. That can be done.
The other interpretation is about vowel sounds, which will reduce the count for words of Nuxalk like "lh" which is one sound [ɬ], "th" and "ng" in English when they are the sounds [θ, ŋ]. This brings us to Nuxalk (Bella Coola) and Tamazight (in the broadest sense) = Berber, and potentially Kabardian. These are languages said to have few or no vowels. However, if you listen to Kabardian, you would not think "Gosh, that language has no vowels!", you would hear dozens of vowels. So we have to talk about "vowel sounds" in at least two different ways, one being phonological where the question is "do we look at the 'phonemic' representation of the word" and the other being based on actual physical output. The claim about Kabardian is kind of based on analytic trickery of phonemicisation, so that language is not all that exotic.
The problem with answering the question at the phonetic level is that there isn't a well-justified phonetic definition of "vowel" as distinct from "consonant release" that doesn't presuppose a particular analysis of these languages (or similar languages). "tsskʃftstt" is a word of the Tashlhiyt dialect said to have no vowels, but does it have a bunch of voiceless schwas or does it have no vowels and a bunch of noisy consonants that simply sound like there are surrounding vowels? Languages do have voiceless vowels (Comanche, but should we not count them as vowels? Is there a vowel in the ordinary casual pronunciation of "potato" – [pʰtʰɛɪɾoʊ] or [pʰə̥tʰɛɪɾoʊ]?
Reliance on raw sound is not a tenable approach, IMO, because there's no language-independent definition of "vowel" based on pure physical sound that doesn't either arbitrarily declare that voiceless vowels aren't vowel, or else force consonants to often be declared to be consonant plus vowel sequences because the consonant has some amount of release.
That all said, the previously-posted Nuxalk example seems to win the prize at least based on current linguistic literature 13 vs 10. The Nuxalk word apparently actually includes an enclitic /kʷt͡sʼ/, perhaps clitics can also be tacked on to the Tashlhiyt word to make it longer.
