The combustion is supposed to be complete in the burner cans/annular space radially outboard of the turbine. There may well be hot spots or streaks near each fuel injector, but the ideal is that the flow is are mixed-out before entering the narrower U-turn passage and certainly before the flow reaches the turbine face. I don't think there is much swirl in the burner space (there is certainly some given the lack of stator vanes to deswirl the compressor outflow)...but I'm not familiar enough with the design of the burner cans (inlet vanes? baffles?) to comment. Ideally you want combustion occurring at low Mach numbers (certainly less than M .2, ideally less than M 0.1) for best performance (limit thermal choking), and high swirl velocity (tangential velocity) in the burner would create a higher Mach no.