I've never cleaned a freewheel in my life. If I had one that was acting like it was gunky, I would just spray some Tri-Flow or One-Lube into it. (NOT WD-40!!!!)
I wouldn't try to take it apart because there are like 10 billion tiny ball bearings inside freewheels that you can't put back in.
I have probably broken 2 or 3 freewheels in about 7 years of riding freewheels (before switching to a freecoaster) and know for a fact that freewheels do regularly 'wear out' so sometimes it is just time to replace it. About 12 bucks for a new one.