A simple call to memory_get_peak_usage() shows Flarum using 4.8-5.6 MB per request. You can see it for yourself if you edit index.php and api.php and add the following at the end of the file:
header('X-Mem: ' . memory_get_peak_usage());
It's surprising because that's a lot more than phpBB 3.2 on the same machine, 2.8-3.5 MB per request. XenForo uses 3.3-3.6 MB.