Yep, indeed!

Most of the "regulars" on my board are in a non-standard user group (called, in fact, "regulars"). Those were the people who were having problems (they were banned). Once I edited your CMS file and added the appropriate user group to the allowed list, that problem was solved.
Secondly, I currently don't use unicode for storing user names in vB, yet I initially was testing the access with a user name that contained an umlauted character ('?'). vBulletin allows such characters to be used even though unicode is not on, but apparently ASCII encoding of such characters confused FlashChat login. I need to look into converting user names into unicode so that any new user who will pick a user name containing an umlauted character will also be able to access FlashChat.
In any case, thanks for the updated CMS file!!