One of the things I found when I went to make my first couple frock coats is that there roughly no tutorials on exactly how you put together the vent on a working suit sleeve. So, during the process of stitchripping over a dozen assorted blazers for the Franken-frock project, I paid attention to how the sleeves were constructed. I'm not saying this tutorial is the only way to do it--or even the right way--but it'll work.
None of them had working buttons, of course, but the construction is close enough--the main difference is in the lining.
Alright. Your sleeve pieces should look approximately like this. When you draft, you need to add enough length to double up on the vent. If you didn't, you can always sew on a piece to be the facing.
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