My favorite religious text: And also a pretty good in-context example of (humorously) clunky writing.
One of the quickest ways to detect 'clunkiness' is ask a good reader to read your story out loud to you. (It helps if they haven't seen it before.) Provided it's printed out clearly and there are no misspellings to trip them up, listen to what it sounds like. And pay careful attention to where they DO trip up. That's likely to be a clunky bit. It's especially useful to note the places where they pause where they shouldn't pause, or don't pause where they should. If they have to start a sentence over again, that's a real red flag spot. If you don't have this kind of articulate friend, you can leave your own work for a while (to where you've kind of forgotten what you wrote) and then read it out loud to yourself. You can even record it and listen to the playback. See where YOU trip up. "Clunky" writing isn't easy to define, except to say it just doesn't read smoothly. Sometimes it's ungrammatical, but it can be perfectly grammatical and still be clunky. Long-windedness or words that don't fit together very well can make it clunky. So can an awkward juxtaposition of clauses. Throw Mama from the train a kiss. As opposed to : Throw Mama a kiss from the train. In our face-to-face writing group, I often get called to read another member's stories out loud, because she has difficulties with her vision. She is a really good writer, and I'm a fairly experienced reader, so it usually goes well. However, if the writing gets clunky I do trip up, and she takes note. It does work as a clunk-detection method. I'm just looking for the courage to get somebody else to read mine out loud!
The second example is perfect. I didn't even read past 'verily'. I just gave up. Clunky writing does that to you.
When I describe writing as clunky, it means 'awkward.' Usually because there are too many clauses and/or the word order is unnatural. It's writing you have to pause and re-read before you can understand what it's trying to say. Good writing flows smoothly, like someone sliding down a water chute. Bad writing judders and halts, like someone bumping down a rocky cliff edge without any butt padding.
Perhaps clunky writing is not always bad. If done purposely and skilfully, it can it be very effective. I think I did something in dialogue once, where the character was stuttering and babbling out of anxiety. And I could follow the religious text example. I read it all without stopping and getting frustrated.