When I flag an answer as a ♦ moderator, the flag button/link becomes hidden. Granted, it's not an option I use very often, but flagging as VLQ/NAA might work if you want the community to decide on the fate of a post, and flagging for moderator attention might work as a means of communication to your colleagues.
What happens under water is that the flag button element gets a
display: none; style. This doesn't happen when flagging as a regular user.
(Tested on the latest Safari and Firefox on macOS Mojave; I'm sure that there are no userscripts involved.)