What could cause my plugin’s options/settings page not to load?

If i had to venture a guess at the cause of the problem my initial thought would be toward the flush rules call.

As Andy said, having debug on helps a great deal, and if you really don’t want to see the errors, you can always use the debug log instead, using the following in your config file..

define('WP_DEBUG', true);          // Turn on debug mode
define('WP_DEBUG_LOG', true);      // Logs errors to wp-content/debug.log
define('WP_DEBUG_DISPLAY', false); // Disable displaying errors

With regard to your settings update not redirecting, typically that occurs when the nonce(s) are missing or incorrect, though i’ll admit it could be something else in your case.

Any errors shown with debug on? (or in the log if you’re using that method?)