D*Alex is right. If you decide to screw a threaded cog onto a freewheel hub and use a bb lockring to secure it, the two MUST be locked up VERY tight. This cannot be over emphasized. The force of resisting the forward motion of fixed gear cranks is very great and will unscrew even an apparently securely locked cog in an instant. I have a fixed/free flip flop hub with the preferable thread setup, right hand normal freewheel thread for the cog, left hand thread for a track lockring on one side. The other side is normal freewheel threading all the way. When I got the shop to put the next smaller cog on the track side I had them put the old cog on the freewheel side with a bb lockring (their suggestion). I still haven't had the courage to even try it. A hub that will take a true track lockring is really the best way.

In response to your earlier question, which may have been answered already. Freewheel threads happen to be the same as English bottom bracket so using lockring just happens to work. It is not the same as the freewheel lockring and has nothing to do with your existing bb.

And you MUST use a nutted axle. You simply cannot get a quick release tight enough to resist those same forces. And the nuts must be tighter than you think they need to be. I thought mine were tight enough, but after a few miles the wheel had moved enough to throw the chain - not fun at all on a fixed gear.

Sorry for recovering some old turf. Some of the concepts in bike mechanics are very simple - once you understand them. But initially it can be hard to get a handle on them. It probably took months before I finally understood the whole freewheel/freehub/cassette issue.