Cloudinary's WordPress plugin indeed supports multisites.
There are two options that you can choose from:
- Using a different Cloudinary account for each site
- Sharing the same Cloudinary account for all sites
For both options you should (for each WordPress site) go to the "Settings" option in the left menu of your WordPress admin interface, and enter the
CLOUDINARY_URL as appears in the dashboard of Cloudinary's Management Console.