You do not have to run Tomcat with Apache unless you are gonna do Http redirects. use the httpbind package that somes with it and then add the JWChat package and you will be off and running, really really simple to be honest, just read the README’‘s and you’'ll have it running an a couple of hours. Word of caution though, if you expect to lock Wildfire down to SSL/TLS only you might have to run Apache as well, to handle the encrypted connection. All in all, if you are running a server that allows all three methods of connection, JWChat is actually sort of easy to install and make work.
Wildfire does not yet support HTTP-Bind so you may want to use the jwchat.war version and deploy it in Tomcat. There are some things you must configure and modify within JWChat so that it runs fine together with Wildfire, these can be found in the JWChat forum.