OK, it's a chonda with a Ruixing carburetor. I'm not really familiar with the GX200, but that is Honda's 6.5 hp engine, so I'd guess that's what it is copied from. Hopefully someone will confirm this for us. It doesn't look like a GX160, which is only 5.5 hp in any case.
Because the plug is black, indicating rich running, and applying the choke doesn't help, I don't think a carburetor or fuel supply fault is the most likely cause of this problem. I suggest you start off by looking for an ignition fault, and move from there to an internal engine fault if necessary. That means finding a way to check for spark. How long is it after it flames out, before you can restart it? If it restarts immediately, we are going to have to use an in-line spark tester to check the ignition system, but if it takes a minute or more to recover after flame-out, you can quickly remove the spark plug, then do a spark test, immediately after it stops.
