Object Cache Pro works great with Multisite Networks out of the box.
All sites in a network share data, such as users and transients, and all cache data is stored in the same Redis database. Due to that, by default, when flushing the cache then entire Redis database is cleared.
To modify this behavior, see the
flush_network configuration option, to either flush only the data for an individual site, or for global groups in addition to an individual site.
This option will also enable the "Flush" site action under Network Admin > Sites.
You may regardless of
flush_network configuration option use the WP CLI to flush the data of an individual site.