Are there some public statistics on how long it takes to process flags on each SE site?
There are no public statistics; posts like 2021: a year in moderation contain related statistics but not flag handling time. Shog9 posted a graph once: How long does it take on average for moderator flags to be handled here on Meta Stack Exchange? but that was just for a single site.
♦ moderators can see it on their dashboard (example), but that probably only includes flags that can be handled by moderators from the dashboard, so it does not include close flags. I know many sites where the moderators prefer to leave VLQ/NAA flags alone (unless they're obvious) and let the community handle them via the Low Quality Posts review queue, which increases handling time. A site that sees a lot of obvious spam, and relatively few other flags, will likely have a low average handling time thanks to SmokeDetector and friends. So all in all, I think those statistics aren't that useful. Maybe if you'd break them down by flag type?