I use a cutting torch only rarely. And getting to see someone else
use a torch (and looking over their shoulder) is even rarer for me.

When I try to cut anything more than a thin plate (say over 1/4 inch
thick) the slag flows behind the cutting tip and into the cut. I
spend too much time trying to recut the slag. I have tried different
angles of holding the cutting tip relative to the part to be cut with
no noticeable improvement. Knowing that skilled people can cut thru
plates that are numerous inches thick with the right equipment - I
figure that I should be able to do better also.

If you are inclinded to ask what brand/model/tip size of a torch - I
don't know much more than my primary torch is a Victor and pretty good
sized and my second torch (came with a collection of welding stuff I
bought at auction) is a Meco (also midsized). I am at work and my
workshop is 10 miles from home and I will not be there until Wednesday
evening when I want to cut a plate. FWIW, recently I used the Meco
for the first time and I had the same issue of the slag flowing behind
the tip and into the kerf.