I recently read about the ability for 10k users to see chat flags network-wide.
Now, my question:
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You need 10k network reputation to see flags on the network chat site, as reported on your chat profile. This value is your combined reputation across all sites, but starts excluding your reputation from low-participation sites (i.e. ones where you have less than 200 reputation) once you pass the association bonus threshold on any particular site, to prevent abuse.
Naturally you need 10k on the respective site for the two per-site chats (Stack Overflow and Meta Stack Exchange).