BuddyPress.org

The BP-Gallery plugin by BuddyDev.com is your best bet; it’s still in beta though.

Also, it’s a paid plugin. Cheapest membership rate is $30 for 3 months access to the entire plugin and theme gallery.

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There’s also MrMaz’s BP-Links plugin – https://wordpress.org/extend/plugins/buddypress-links/.

And oEmbed for BuddyPress – https://wordpress.org/extend/plugins/oembed-for-buddypress/

Both of these plugins rely on third-party video sites like YouTube, DailyMotion, etc.