Long time ago, I know, but the cache clear procedure on FF 31.0/Windows works for me - maybe it's new. Options -> network -> cached web content -> clear now. Shut down FF, restart. No messing about with SqLite, new favicon loads.
However, there is another potential problem. The server for the site which I was trying to refresh the icon for had a DocumentRoot of /var/www. This site was at foo.com/fubar, where var/www/fubar symlinked to somewhere else. In other words, the site is one level down from DocumentRoot. This works for Chrome, Opera, and IE, but not Safari or FF:
FF looks for the favicon in /var/www, instead of /var/www/fubar. This works for all 5 browsers:
