This channel?
https://www.youtube.com/channel/UC3ZSElstgflUtJGL2pKu9Ng
So you want to look in the Wayback Machine for his
legacy URL:
https://www.youtube.com/user/DukeLovesYou
Which has a lot of results:
However this is just for the profile, you'll still need to find the video, which could be featured on there, or in the
/videos page (you'll need that URL for the Wayback).
If you find the video and it can be played, it is stored, and so you will be able to download it.
I'm also looking for one, a clip from Inception of nardo dicap (voiced by duke) dramatically explaining to ellen page what constitutes a juggalo.
Don't know if this is, I just noticed he had a favourite with some words that match your post, but the video is unavailable, currently privated.
https://www.youtube.com/watch?v=cHL4k2whF00
In any case, you could then use
https://findyoutubevideo.thetechrobo.ca/ to see if the video has been archived in several sites, and this is the case for that one:
But anyways, maybe it's another one, the point is that you can use this website to see if some archive exists for that, for popular archiving sites.
In either case, finding what you want may be doable, but it's going to take a bit of digging, these are some of the tools you can use.