If I got a copyright claim...

[NicsterV]

If I got a copyright claim on a vine compilation video I made (I don't own any of the content, so it's fine that I'm not making money from it) could someone else who owns one of the other vine videos in my compilation take my video down? Or no, because someone else who made one of the other videos already claimed copyright.. I'm confused.

 

[Shakycow]

I don't own any of the content, so it's fine that I'm not making money from it

Not even remotely true. It doesn't matter if you're making income from it or not, if you don't own it, you legally can't post it.

...could someone else who owns one of the other vine videos in my compilation take my video down?

Absolutely. Anyone who has any connection to any of the videos involved can have a take-down notice issued and you'll get a copyright strike.

 

[RyanH]

Vine compilations very rarely get taken down, just Content ID matched by networks like Fullscreen and Collab.

Regardless, if you don't have permission from all of the Viners who's content you used, you're infringing their copyright.