What is the longest one-syllable word?

Screeched, stretched, and scratched

Strengths has the same number of letters and only one vowel.

Longest Monosyllabic English Words:

"Scraunched", meaning to crush or crush noisily, and the archaic word "strengthed", each 10 letters long, are the longest English words that are only one syllable long. There are more 9-letter words: "scratched", "screeched", "scrounged", "squelched", "straights", and "strengths".

fwointl.com/artman/publish/printer_493.shtml (webpage no longer exists)

The one most commonly cited is screeched (nine letters). However, one ought to mention also scratched, scrounged, scrunched, stretched, and the plural nouns straights and strengths (all with nine letters).

The complete Oxford English Dictionary also indicates the existence of scraughed, scrinched, scritched, scrooched, sprainged, spreathed, throughed, and thrutched.

askoxford.com/asktheexperts/faq/aboutwords/onesyllable (webpage no longer exists)

There are two: squirrelled and broughammed

https://en.wikipedia.org/wiki/List_of_the_longest_English_words_with_one_syllable

What is the longest one-syllable English word:

The one most commonly cited is screeched (nine letters). However, one ought to mention also scratched, scrounged, scrunched, stretched, and the plural nouns straights and strengths (all with nine letters). The complete Oxford English Dictionary also indicates the existence of scraughed, scrinched, scritched, scrooched, sprainged, spreathed, throughed, and thrutched. The OED also cites a single instance of the ten-letter word scraunched, from the 1620 English translation of Don Quixote.

https://www.lexico.com/explore/what-is-the-longest-one-syllable-english-word

So depending on what you count as a word, it may be scraunched at ten letters, or any of the 9 letter words listed above.

This is a debatable question.

The original French name for smurf is schtroumpf, and is used as an all-purpose noun and verb by Smurfs and in imitation of them. The form schtroumpfed is used in Alistair McEwen's English translation of an essay by Umberto Eco: "Let us suppose that an English speaker of average culture hears a Schtroumpf poet reciting I schtroumpfed lonely as a schtroumpf." However, this is intended to represent the Schtroumpf language rather than English. That one syllable word is twelve letters.

The eleven-letter word broughammed (created from brougham by analogy with bussed, biked, carted etc.), while readily pronounceable as one syllable in all dialects ("broomed", IPA: /bɹu¢°md/), is yet to appear in a print dictionary. See: "ough" words. The word might also be spelled broughamed, with ten letters.

Squirrelled is the spelling in British English of a word usually spelled in American English as squirreled (see -led and -lled spellings) . While in Received Pronunciation the word has two syllables (IPA: /ˈskwɪɹəɫd/), it is often pronounced /skwɝɫd/ (rhymes with world) in North American English [1]. Of those who use the one-syllable pronunciation, some may use the eleven-letter spelling; for the rest, it is a ten-letter monosyllable.

https://en.wikipedia.org/wiki/List_of_the_longest_English_words_with_one_syllable

This man votes for scraunched.

At ten letters long, this pseudo-onomatopoeic synonym for crunched is the longest monosyllabic word in the English language. All six of its closest rivals — scratched, screeched, scrounged, squelched, straights, and strengths — curiously also begin with the letter S, but each of them falls short of the champion of monosyllabry’s deliciously burnished mouthfeel. Just say it a few times and you’ll understand. How can so many letters voiced in a single beat be blended any more smoothly?

http://www.guinnessworldrecords.com/world-records/longest-monosyllabic-english-words/

According to Wikipedia, depending on your dialect and whether you accept words from other languages, the longest monosyllabil word in English can have up to 11 leters.

My own candidate is the American English pronunciation of "squirrelled" (11 letters).

https://en.wikipedia.org/wiki/List_of_the_longest_English_words_with_one_syllable