I don't consider myself to be a complete idiot, so since I was getting confused by something I guess I'll point this out for other users. Although Paul says to install the chat in your forum root directory (ie. folder with usercp.php) he means to put the unzipped CHAT directory into the root directory. In other words don't open the flash chat CHAT directory and dump all the files into your forum root directory, some files will end up being overwritten, and this isn't how it's supposed to be done.
I was curious why Paul was asking to install it into the forum root directory, but he means the CHAT folder, not all the CHAT folder files.

Just figured I'd mention this since I was about to make a mess since I thought even though it was going to look ugly, for some reason he made it this way.

Not true, and that's why some of you are having problems with the install.
All you do is unzip the flash chat that you downloaded, you'll see a CHAT directory, put that directory and it's contents into your forum directory. Yes it did need some clearing up.

Thanks for this integration Paul!!