I have your exact bike 1993 kx 125 and had the exact problem. I cleaned the power valve (that wasn't gunked at all) and still had the problem.
There is an O-ring on a round seal held in by a screw behind that plastic cover with the rubber boot (part 92055A on the part diagram). Replace it and you should be good to go.
I just used an o-ring out of a refrigerant kit I bought for $9.99 at Harbor freight. Came with a couple hundred o-rings at many different sizes. Don't waste your money on the OEM for a few $$$ for 1 o-ring.
The o-ring i used was slightly larger in thickness and smaller in diameter by just a hair, but stretching it made it about the same size. Not the same as they call for, but all it does is keep that burnt oil from leaking out. It is nothing critical. I rode mine for the longest time just making a mess, not sure why it was leaking.
God Bless!
Stang.