If you switch your includes/database.php to use the mysqli version, Fireboard's config section in Joomla admin starts outputting errors like

[code:1]mysql_num_rows(): supplied argument is not a valid MySQL result resource[/code:1]

That's b/c administrator/components/com_fireboard/admin.fireboard.php is using mysql_query instead of Joomla's built-in database functions. And when you switch Joomla to start using mysqli, then mysql_query will fail because mysql_connection doesn't get called anymore. I think.

Anyhow, the fix is to replace

[code:1]if (mysql_num_rows(mysql_query("SHOW TABLES LIKE '" . $table_nm . "'"«»))) {[/code:1]

with

[code:1]if (in_array($table_nm, $database->getTableList())) {[/code:1]

around lines 64 and 2230

So...hopefully that can get incorporated into the next release. Lmk if there are more official ways of submitting fixes.