You can use a game updater which downloads the PKG files to your computer and tells you what firmware it is, or you can use multiMAN's game updater which also tell you what firmware the update is but after you download it.
I might not understand you correctly, but here is my take on your problem:
It seems there is confusion between DLC and game updates. DLC generally are add-ons for for games to enable additional content to a game. This allows you to play additional "chapters" (for lack of a better word). Game updates are generally bug fixes, stability fixes, etc to allow for "smAoother" gameplay without adding anything extra to a game compared to what it is like hwne you purchased it.
As a rule of thumb, you can not get DLC if you have a jailbroken PS3, but you should be able to get game updates in the form of PKG's.
I remember seeing a Black Ops DLC for users on CFW before . You install it like any other .PKG file but you would also have to move an activation file to somewhere on your PS3s Internal HDD before you start the game every time.
But other than that I don't think there are any other DLC available for CFW users.